Mensuration Class 8 | Most Important Notes, Formula And MCQs

Mensuration Class 8 Notes, Formula, MCQs & NCERT Solutions

Table Of Content ( Mensuration Class 8 )

Part 1

Mensuration Class 8
Introduction
Table of Contents
Abbreviations
Complete Theory
Hindi + English Explanation
Formula Table
Key Points

Part 2

Solved Examples

Part 3

50 MCQs

Part 4

HOTS
Assertion Reason
Case Study

Part 5

Word Problems
Fill in the Blanks
True False
Match the Following

Part 6

NCERT Exercise Complete Solution

Part 7

FAQs
PYQs
Revision Notes

Part 8

Conclusion
previous topic : Algebraic expression

Introduction (English) ( Mensuration Class 8 )

Mensuration is one of the most scoring chapters in Class 8 Mathematics. It helps us calculate the perimeter, area, surface area, and volume of different geometrical figures. The concepts of mensuration are widely used in engineering, architecture, construction, agriculture, sports, and everyday life. ( Mensuration Class 8 )

Students preparing for CBSE, State Board, Olympiads, and competitive exams should master this chapter because formula-based questions are frequently asked.

परिचय (Hindi)

Mensuration (मापन) गणित का एक महत्वपूर्ण अध्याय है जिसमें विभिन्न आकृतियों का परिमाप (Perimeter), क्षेत्रफल (Area), पृष्ठीय क्षेत्रफल (Surface Area) तथा आयतन (Volume) ज्ञात किया जाता है।

यह अध्याय केवल परीक्षा के लिए ही नहीं बल्कि हमारे दैनिक जीवन में भी अत्यंत उपयोगी है।

उदाहरण—

घर बनवाने में
खेत की माप करने में
पानी की टंकी का आयतन निकालने में
दीवार पर पेंट कराने में
फर्श पर टाइल लगाने में

What is Mensuration?

English

Mensuration is the branch of mathematics that deals with the measurement of geometric figures and solids.

It helps us find

Length
Breadth
Height
Area
Perimeter
Surface Area
Volume

Hindi

Mensuration गणित की वह शाखा है जिसमें विभिन्न आकृतियों और ठोस वस्तुओं का मापन किया जाता है।

इसके द्वारा हम ज्ञात करते हैं—

लंबाई
चौड़ाई
ऊँचाई
परिमाप
क्षेत्रफल
पृष्ठीय क्षेत्रफल
आयतन

Why is Mensuration Important?

English

Mensuration helps in

Construction work
Interior designing
Painting walls
Farming
Road construction
Water storage
Architecture
Engineering

Hindi

Mensuration का उपयोग—

मकान बनाने में
पेंटिंग कराने में
खेती में
सड़क निर्माण में
इंजीनियरिंग में
वास्तुकला में
जल संग्रहण में

Daily Life Applications ( Mensuration Class 8 )

Situation	Use of Mensuration
Painting a wall	Area
Fencing a garden	Perimeter
Water Tank	Volume
Tile Flooring	Area
Swimming Pool	Volume
Boundary Wall	Perimeter
Packaging	Surface Area
Agriculture	Area

Abbreviations ( Mensuration Class 8 )

Short Form	Full Form
cm	Centimetre
m	Metre
km	Kilometre
mm	Millimetre
sq.	Square
cu.	Cubic
TSA	Total Surface Area
CSA	Curved Surface Area
LSA	Lateral Surface Area
Vol.	Volume
Peri.	Perimeter

Important Definitions ( Mensuration Class 8 )

1. Perimeter (परिमाप)

English

Perimeter is the total length of the boundary of a closed figure.

Hindi

किसी बंद आकृति की चारों ओर की कुल लंबाई को परिमाप कहते हैं।

2. Area (क्षेत्रफल)

English

Area is the region enclosed inside a closed figure.

Hindi

किसी आकृति द्वारा घिरे हुए भाग का माप क्षेत्रफल कहलाता है।

3. Surface Area (पृष्ठीय क्षेत्रफल)

English

The total area covering the outer surface of a solid object.

Hindi

किसी ठोस वस्तु की बाहरी सतह का कुल क्षेत्रफल।

4. Volume (आयतन)

English

Volume is the amount of space occupied by a solid.

Hindi

किसी ठोस वस्तु द्वारा घेरा गया स्थान आयतन कहलाता है।

Types of Plane Figures ( Mensuration Class 8 )

Shape	Description
Square	Four equal sides
Rectangle	Opposite sides equal
Triangle	Three sides
Circle	Round figure
Parallelogram	Opposite sides parallel
Rhombus	Four equal sides
Trapezium	One pair of parallel sides

Types of Solid Shapes ( Mensuration Class 8 )

Shape	Description
Cube	All edges equal
Cuboid	Rectangular box
Cylinder	Circular ends
Cone	One circular base
Sphere	Ball-shaped
Hemisphere	Half sphere

SI Units ( Mensuration Class 8 )

Quantity	SI Unit
Length	metre (m)
Perimeter	metre (m)
Area	square metre (m²)
Surface Area	square metre (m²)
Volume	cubic metre (m³)

Unit Conversion Table ( Mensuration Class 8 )

Conversion
10 mm = 1 cm
100 cm = 1 m
1000 m = 1 km
1 m² = 10000 cm²
1 cm² = 100 mm²
1 m³ = 1000000 cm³
1000 L = 1 m³

Formula Chart ( Mensuration Class 8 )

Square

Perimeter = 4 × side

Area = side²

Rectangle

Perimeter = 2(l + b)

Area = l × b

Triangle

Perimeter = Sum of all sides

Area = ½ × base × height

Parallelogram

Area = base × height

Perimeter = 2(a + b)

Trapezium

Area = ½ × (sum of parallel sides) × height

Circle

Circumference = 2πr

Area = πr²

Cube

TSA = 6a²

LSA = 4a²

Volume = a³

Cylinder

CSA = 2πrh

TSA = 2πr(r + h)

Volume = πr²h

Memory Tricks ( Mensuration Class 8 )

Area → Inside

Think of painting the floor.

Perimeter → Outside

Think of fencing a garden.

Volume → Inside Space

Think of filling a water tank.

Surface Area → Outside Cover

Think of wrapping a gift.

Exam Tips ( Mensuration Class 8 )

Write formulas before solving.

Always mention units.

Convert units first if different.

Draw diagrams wherever possible.

Do rough calculations separately.

Common Mistakes Students Make

Forgetting to convert units.
Writing area in cm instead of cm².
Writing volume in cm² instead of cm³.
Using wrong formula for trapezium.
Confusing perimeter with area.
Ignoring π value (use 22/7 or 3.14 as instructed in the question).

Key Points (Quick Revision)

Mensuration means measurement of geometrical figures.
Perimeter is the total boundary length.
Area is the enclosed region.
Surface Area is the outer covering of a solid.
Volume is the space occupied by a solid.
Area is measured in square units (cm², m²).
Volume is measured in cubic units (cm³, m³).
Always convert units before applying formulas.
Rectangle area = Length × Breadth.
Triangle area = ½ × Base × Height.
Circle area = πr².
Cuboid volume = Length × Breadth × Height.

Example 1: Perimeter of a Square

Question (English)

Find the perimeter of a square whose side is 12 cm.

प्रश्न (Hindi)

12 सेमी भुजा वाले वर्ग का परिमाप ज्ञात कीजिए।

Solution

Formula:

Perimeter = 4 × Side

= 4 × 12

= 48 cm

Answer: 48 cm

Example 2: Area of a Square

Question

Find the area of a square having side 15 cm.

Solution

Formula:

Area = Side²

= 15²

= 225 cm²

Answer: 225 cm²

Example 3: Perimeter of a Rectangle

Question

Length = 18 cm

Breadth = 10 cm

Find the perimeter.

Solution

Perimeter = 2(l + b)

= 2(18 + 10)

= 56 cm

Example 4: Area of a Rectangle

Length = 16 cm

Breadth = 9 cm

Area = l × b

= 16 × 9

= 144 cm²

Example 5: Area of a Triangle

Base = 20 cm

Height = 8 cm

Area = ½ × Base × Height

= ½ × 20 × 8

= 80 cm²

Example 6: Perimeter of a Triangle

Sides = 8 cm, 10 cm, 12 cm

Perimeter

= 8 + 10 + 12

= 30 cm

Example 7: Area of a Parallelogram

Base = 15 cm

Height = 12 cm

Area = Base × Height

= 15 × 12

= 180 cm²

Example 8: Area of a Trapezium

Parallel sides = 18 cm and 10 cm

Height = 7 cm

Area

= ½ × (18 + 10) × 7

= 98 cm²

Example 9: Circumference of a Circle

Radius = 7 cm

Circumference

= 2πr

= 44 cm

Example 10: Area of a Circle

Radius = 14 cm

Area

= 22/7 × 14 × 14

= 616 cm²

Example 11: Total Surface Area of a Cube

Side = 6 cm

TSA = 6a²

= 6 × 6²

= 216 cm²

Example 12: Volume of a Cube

Side = 8 cm

Volume = a³

= 8³

= 512 cm³

Example 13: Total Surface Area of a Cuboid

Length = 8 cm

Breadth = 5 cm

Height = 4 cm

TSA

= 2(lb + bh + hl)

= 184 cm²

Example 14: Volume of a Cuboid

Volume

= l × b × h

= 160 cm³

Example 15: Curved Surface Area of a Cylinder

Radius = 7 cm

Height = 10 cm

CSA

= 2πrh

= 440 cm²

Example 16: Total Surface Area of a Cylinder

Radius = 7 cm

Height = 10 cm

TSA

= 2πr(r + h)

= 748 cm²

Example 17: Volume of a Cylinder

Radius = 7 cm

Height = 10 cm

Volume

= πr²h

= 1540 cm³

Concept-Based Questions ( Mensuration Class 8 )

Question 1

Why is area measured in square units?

Answer

Because area measures a two-dimensional surface, so both length and breadth are multiplied.

क्योंकि क्षेत्रफल दो विमाओं (लंबाई और चौड़ाई) का गुणनफल होता है, इसलिए इसे वर्ग इकाई (Square Unit) में मापा जाता है।

Question 2

Why is volume measured in cubic units?

Answer

Volume measures three-dimensional space.

आयतन लंबाई, चौड़ाई और ऊँचाई तीनों का गुणनफल होता है, इसलिए इसे घन इकाई (Cubic Unit) में मापा जाता है।

Question 3

Can two figures have the same area but different perimeters?

Answer

Yes.

Different shapes can enclose the same area while having different boundary lengths.

Question 4

Can two figures have the same perimeter but different areas?

Answer

Yes.

Example:

Rectangle

8 × 2

Perimeter = 20

Area = 16

Rectangle

5 × 5

Perimeter = 20

Area = 25

Think and Solve ( Mensuration Class 8 )

Question 1

A square and a rectangle have the same perimeter.

Which one has the larger area?

Answer

The square has the maximum area for a given perimeter.

Question 2

Why do engineers calculate surface area before painting a building?

Answer

Because paint is applied only on the outer surface.

Question 3

Why is perimeter important while fencing a garden?

Answer

Because fencing is done around the boundary.

Exam-Oriented Practice Questions ( Mensuration Class 8 )

Find the perimeter of a square whose side is 25 cm.

Answer: 100 cm

Find the area of a rectangle of length 15 cm and breadth 9 cm.

Answer: 135 cm²

Find the area of a triangle having base 18 cm and height 12 cm.

Answer: 108 cm²

Find the circumference of a circle of radius 21 cm.

Answer: 132 cm

Find the area of a circle having radius 7 cm.

Answer: 154 cm²

Find the volume of a cube of side 9 cm.

Answer: 729 cm³

Find the total surface area of a cube having side 5 cm.

Answer: 150 cm²

Find the volume of a cuboid of dimensions 8 cm × 6 cm × 5 cm.

Answer: 240 cm³

Find the area of a trapezium whose parallel sides are 16 cm and 10 cm and height is 8 cm.

Answer: 104 cm²

Q10

Find the curved surface area of a cylinder having radius 14 cm and height 12 cm.

Answer: 1056 cm²

Formula Application Tips ( Mensuration Class 8 )

Figure	Remember This Formula
Square	Area = a²
Rectangle	Area = l × b
Triangle	Area = ½ × b × h
Circle	Area = πr²
Cube	Volume = a³
Cuboid	Volume = l × b × h
Cylinder	Volume = πr²h
Trapezium	Area = ½ × (a + b) × h

Quick Revision ( Mensuration Class 8 )

Perimeter → Boundary length
Area → Inside region
Surface Area → Outside covering
Volume → Space occupied
Square Area = a²
Rectangle Area = l × b
Triangle Area = ½bh
Circle Area = πr²
Cube Volume = a³
Cuboid Volume = lbh
Cylinder Volume = πr²h

Easy Level MCQs ( Mensuration Class 8 )

1. The perimeter of a square having side 8 cm is:

A) 24 cm
B) 32 cm
C) 64 cm
D) 16 cm

Answer: ✅ B) 32 cm

2. Area of a square with side 12 cm is:

A) 24 cm²
B) 48 cm²
C) 144 cm²
D) 120 cm²

Answer: ✅ C) 144 cm²

3. Area of a rectangle is calculated by:

A) l + b

B) l × b

C) 2(l + b)

D) l²

Answer: ✅ B

4. Perimeter of a rectangle is:

A) l × b

B) l²

C) 2(l + b)

D) b²

Answer: ✅ C

5. Area of a triangle is:

A) b × h

B) 2bh

C) ½ × b × h

D) b + h

Answer: ✅ C

6. Which unit is used for area?

A) cm

B) cm²

C) cm³

D) litre

Answer: ✅ B

7. Which unit is used for volume?

A) cm

B) cm²

C) cm³

D) metre

Answer: ✅ C

8. Which quantity measures the boundary of a figure?

A) Area

B) Volume

C) Perimeter

D) Height

Answer: ✅ C

9. Which symbol represents pi?

A) θ

B) α

C) π

D) β

Answer: ✅ C

10. Value of π generally taken in Class 8 is:

A) 3

B) 22/7

C) 7/22

D) 2

Answer: ✅ B

Moderate Level MCQs ( Mensuration Class 8 )

11. The area of a rectangle of length 15 cm and breadth 8 cm is:

A) 120 cm²

B) 46 cm²

C) 240 cm²

D) 92 cm²

Answer: ✅ A

12. The perimeter of a rectangle whose length is 12 cm and breadth is 7 cm is:

A) 19 cm

B) 38 cm

C) 84 cm

D) 24 cm

Answer: ✅ B

13. Area of a triangle having base 18 cm and height 10 cm is:

A) 180 cm²

B) 90 cm²

C) 280 cm²

D) 80 cm²

Answer: ✅ B

14. Circumference of a circle with radius 7 cm is:

A) 22 cm

B) 44 cm

C) 154 cm

D) 88 cm

Answer: ✅ B

15. Area of a circle with radius 14 cm is:

A) 308 cm²

B) 616 cm²

C) 196 cm²

D) 154 cm²

Answer: ✅ B

16. Volume of a cube having side 6 cm is:

A) 36 cm³

B) 216 cm³

C) 72 cm³

D) 108 cm³

Answer: ✅ B

17. TSA of a cube of side 5 cm is:

A) 150 cm²

B) 125 cm²

C) 100 cm²

D) 25 cm²

Answer: ✅ A

18. Volume of a cuboid measuring 8 cm × 5 cm × 4 cm is:

A) 160 cm³

B) 80 cm³

C) 40 cm³

D) 200 cm³

Answer: ✅ A

19. CSA of a cylinder is:

A) πr²

B) 2πrh

C) 2πr(r+h)

D) πr²h

Answer: ✅ B

20. Volume of a cylinder is:

A) πr²h

B) 2πrh

C) πr²

D) 2πr²

Answer: ✅ A

Higher Order MCQs (HOTS) ( Mensuration Class 8 )

21. A rectangle has length 20 cm and breadth 10 cm. If both dimensions are doubled, its area becomes:

A) Double

B) Triple

C) Four times

D) Eight times

Answer: ✅ C

22. If the side of a square is doubled, its perimeter becomes:

A) Double

B) Triple

C) Four times

D) Half

Answer: ✅ A

23. If the radius of a circle is doubled, its area becomes:

A) Double

B) Four times

C) Eight times

D) Half

Answer: ✅ B

24. If every edge of a cube is doubled, its volume becomes:

A) Double

B) Four times

C) Six times

D) Eight times

Answer: ✅ D

25. Which quantity changes the fastest when dimensions increase?

A) Perimeter

B) Area

C) Volume

D) Length

Answer: ✅ C

Assertion & Reason MCQs ( Mensuration Class 8 )

26.

Assertion (A): Area is measured in square units.

Reason (R): Area is obtained by multiplying two dimensions.

A) Both A and R are true, and R is the correct explanation of A.

B) Both are true, but R is not the correct explanation.

C) A is true, R is false.

D) A is false, R is true.

Answer: ✅ A

27.

Assertion: Volume is measured in cubic units.

Reason: Volume depends on length, breadth, and height.

Answer: ✅ A

28.

Assertion: Perimeter is measured in square units.

Reason: Perimeter measures boundary length.

Answer: ✅ D (Assertion is false, Reason is true.)

29.

Assertion: Surface area is measured in square units.

Reason: It measures the outer surface of a solid.

Answer: ✅ A

30.

Assertion: Volume of a cube = a².

Reason: Cube has equal sides.

Answer: ✅ D (Assertion is false, Reason is true.)

Mixed Practice MCQs ( Mensuration Class 8 )

31. Which shape has four equal sides?

A) Rectangle

B) Square

C) Triangle

D) Trapezium

Answer: ✅ B

32. Which figure has only one curved boundary?

A) Circle

B) Rectangle

C) Triangle

D) Square

Answer: ✅ A

33. Which shape has one pair of parallel sides?

A) Square

B) Rectangle

C) Trapezium

D) Rhombus

Answer: ✅ C

34. A cube has:

A) 4 faces

B) 5 faces

C) 6 faces

D) 8 faces

Answer: ✅ C

35. A cuboid has:

A) 8 vertices

B) 6 vertices

C) 4 vertices

D) 10 vertices

Answer: ✅ A

36. Which formula gives the area of a parallelogram?

A) l × b

B) b × h

C) ½ × bh

D) πr²

Answer: ✅ B

37. Which quantity is needed to find the area of a triangle?

A) Radius

B) Base and Height

C) Side only

D) Diameter

Answer: ✅ B

38. Which formula is used for the area of a circle?

A) 2πr

B) πr²

C) πd

D) 2πr²

Answer: ✅ B

39. A garden is fenced around its boundary. Which concept is used?

A) Area

B) Volume

C) Perimeter

D) Surface Area

Answer: ✅ C

40. Water stored inside a tank is measured by:

A) Area

B) Volume

C) Perimeter

D) Height

Answer: ✅ B

Challenge MCQs ( Mensuration Class 8 )

41. The area of a square is 196 cm². Its side is:

A) 12 cm

B) 14 cm

C) 16 cm

D) 18 cm

Answer: ✅ B

42. The perimeter of a square is 64 cm. Find its side.

A) 8 cm

B) 12 cm

C) 16 cm

D) 20 cm

Answer: ✅ C

43. The volume of a cube is 343 cm³. Find its side.

A) 5 cm

B) 6 cm

C) 7 cm

D) 8 cm

Answer: ✅ C

44. Which unit is NOT suitable for measuring area?

A) cm²

B) m²

C) km²

D) cm

Answer: ✅ D

45. Which formula is correct for the volume of a cuboid?

A) l + b + h

B) l × b × h

C) 2(lb + bh + hl)

D) 2(l + b)

Answer: ✅ B

46. Which formula gives the Total Surface Area of a cylinder?

A) 2πrh

B) πr²h

C) 2πr(r + h)

D) πr²

Answer: ✅ C

47. Which shape has the maximum area for a given perimeter?

A) Rectangle

B) Square

C) Triangle

D) Trapezium

Answer: ✅ B

48. A wall is to be painted. Which measurement is required?

A) Perimeter

B) Area

C) Volume

D) Radius

Answer: ✅ B

49. A water tank capacity is measured in:

A) Square units

B) Cubic units

C) Centimetres

D) Metres only

Answer: ✅ B

50. Which chapter mainly deals with measuring geometrical figures?

A) Algebra

B) Mensuration

C) Statistics

D) Linear Equations

Answer: ✅ B

Quick Revision ( Mensuration Class 8 )

Perimeter → Boundary Length	Area → Covered Region
Surface Area → Outer Surface of a Solid	Volume → Space Occupied
Area → Square Units (cm², m²)	Volume → Cubic Units (cm³, m³)
Use π = 22/7 or 3.14 as directed in the question.	Always write the correct units in the final answer.

Section A: HOTS Questions ( Mensuration Class 8 )

Q1. Same Perimeter, Different Area

Question (English)

Two rectangles have the same perimeter of 40 cm.

Rectangle A: 12 cm × 8 cm

Rectangle B: 15 cm × 5 cm

Which rectangle has the larger area?

Solution

Rectangle A

Area = 12 × 8 = 96 cm²

Rectangle B

Area = 15 × 5 = 75 cm²

Answer: Rectangle A has the larger area.

हिंदी व्याख्या

दोनों आयतों का परिमाप समान होने पर भी उनका क्षेत्रफल अलग-अलग हो सकता है। इसलिए केवल परिमाप देखकर क्षेत्रफल का अनुमान नहीं लगाया जा सकता।

Q2. Doubling the Side

A square has side 9 cm.

If the side is doubled, by how much does the area increase?

Solution

Original Area = 9² = 81 cm²

New Side = 18 cm

New Area = 18² = 324 cm²

Increase = 324 − 81 = 243 cm²

Answer: The area becomes 4 times the original.

Q3. Doubling the Radius

A circle has radius 7 cm.

If the radius becomes 14 cm, how many times does the area increase?

Solution

Area ∝ r²

(14²)/(7²)

= 196/49

= 4

Answer: Four times.

Q4. Doubling the Edge of a Cube

A cube has side 5 cm.

If each edge is doubled, how many times does the volume increase?

Solution

Volume ∝ a³

(10³)/(5³)

= 1000/125

= 8

Answer: Eight times.

Q5. Paint or Fence?

A farmer wants to paint the floor of a rectangular room and also put fencing around his garden.

Which mathematical concepts are used?

Answer

Painting the floor → Area
Fencing the garden → Perimeter

Section B: Case Study Questions ( Mensuration Class 8 )

Case Study 1: Painting a Classroom

A classroom is 12 m long and 8 m wide.

The cost of painting is ₹40 per square metre.

Q1. Find the area of the classroom.

A) 80 m²

B) 96 m²

C) 120 m²

D) 100 m²

Answer: ✅ B

Q2. Total painting cost?

Area = 96 m²

Cost = 96 × 40

= ₹3840

Q3. Which concept is used?

A) Volume

B) Perimeter

C) Area

D) Radius

Answer: ✅ C

Case Study 2: Water Tank

A cuboid water tank measures

Length = 6 m

Breadth = 4 m

Height = 3 m

Q1. Find its volume.

Volume

= 6 × 4 × 3

= 72 m³

Q2. Which unit is correct?

A) m

B) m²

C) m³

D) Litre

Answer: ✅ C

Q3. If the height is doubled, what is the new volume?

6 × 4 × 6

= 144 m³

Section C: Competency-Based Questions

A square field has side 40 m.

A farmer wants to fence it.

How much fencing wire is needed?

Solution

Perimeter

= 4 × 40

= 160 m

A square floor has side 9 m.

Tiles cost ₹120 per square metre.

Find the total cost.

Solution

Area

= 9²

= 81 m²

Cost

= 81 × 120

= ₹9720

A cylindrical water tank has radius 3 m and height 8 m.

Find its volume.

Use π = 22/7.

Solution

Volume

= πr²h

= 1584/7 ≈ 226.29 m³

Section D: Assertion & Reason (Advanced)

Assertion

Area increases when the side of a square increases.

Reason

Area depends on the square of the side.

A) Both are true and Reason correctly explains Assertion.

B) Both are true but Reason is not the correct explanation.

C) Assertion is true but Reason is false.

D) Assertion is false but Reason is true.

Answer: ✅ A

Assertion

Perimeter and area are always equal.

Reason

Both are measured in centimetres.

Answer: ✅ D

Assertion

Volume is measured in cubic units.

Reason

Volume measures three-dimensional space.

Answer: ✅ A

Assertion

Surface area is measured in square units.

Reason

It measures only the boundary of a figure.

Answer: ✅ C

Assertion

A cube and a cuboid have the same formulas.

Reason

Both are three-dimensional figures.

Answer: ✅ B

Section E: Long Answer Questions

Explain the difference between Perimeter and Area.

Answer

Perimeter	Area
Total boundary length	Region enclosed
One-dimensional	Two-dimensional
Measured in cm or m	Measured in cm² or m²
Used in fencing	Used in painting or flooring

Differentiate between Surface Area and Volume.

Surface Area	Volume
Outer covering	Space occupied
Square units	Cubic units
Used in painting	Used in storage capacity

Explain the importance of Mensuration in daily life.

Answer

Mensuration is used in:

House construction
Road construction
Agriculture
Painting
Interior decoration
Swimming pools
Water tanks
Packaging
Engineering
Architecture

Section F: Diagram-Based Questions

Draw a rectangle of length 8 cm and breadth 5 cm.

Find:

Perimeter
Area

Answer

Perimeter = 26 cm

Area = 40 cm²

Draw a square of side 6 cm.

Find:

Area
Perimeter

Answer

Area = 36 cm²

Perimeter = 24 cm

Draw a circle of radius 7 cm.

Find:

Circumference
Area

Answer

Circumference = 44 cm

Area = 154 cm²

Common Exam Mistakes

Forgetting to write units.

Confusing cm² with cm³.

Using the perimeter formula instead of the area formula.

Not converting units before solving.

Using the wrong value of π.

Incorrectly squaring or cubing numbers.

Quick Revision Notes

Perimeter → Boundary length
Area → Inside region
Surface Area → Outer surface
Volume → Space occupied
Area → Square units
Volume → Cubic units
Side doubled → Area becomes 4 times
Radius doubled → Circle area becomes 4 times
Edge doubled → Cube volume becomes 8 times

Word Problems (Basic to Advanced)

Word Problem 1 (Easy)

Question (English)

A square park has a side of 25 m. Find its perimeter.

प्रश्न (Hindi)

एक वर्गाकार पार्क की प्रत्येक भुजा 25 मीटर है। उसका परिमाप ज्ञात कीजिए।

Solution

Formula:

Perimeter = 4 × Side

= 4 × 25

= 100 m

Answer: 100 m

Word Problem 2

A rectangular classroom is 12 m long and 8 m wide. Find its area.

Solution

Area = Length × Breadth

= 12 × 8

= 96 m²

Answer: 96 m²

Word Problem 3

A farmer wants to fence a rectangular field of length 40 m and breadth 25 m. How much fencing wire is required?

Solution

Perimeter = 2(l + b)

= 2(40 + 25)

= 130 m

Answer: 130 m

Word Problem 4

A square floor has a side of 9 m. Tiles cost ₹150 per square metre. Find the total cost.

Solution

Area = 9² = 81 m²

Cost = 81 × 150

= ₹12,150

Answer: ₹12,150

Word Problem 5

A circular garden has a radius of 14 m. Find its area.

(Use π = 22/7)

Solution

Area = πr²

= 22/7 × 14 × 14

= 616 m²

Answer: 616 m²

Word Problem 6

A cube has an edge of 8 cm. Find its volume.

Solution

Volume = a³

= 8³

= 512 cm³

Answer: 512 cm³

Word Problem 7

A cuboid measures 12 cm × 8 cm × 5 cm. Find its volume.

Solution

Volume = l × b × h

= 12 × 8 × 5

= 480 cm³

Answer: 480 cm³

Word Problem 8

A cylindrical water tank has radius 7 m and height 10 m. Find its volume.

Solution

Volume = πr²h

= 22/7 × 7 × 7 × 10

= 1540 m³

Answer: 1540 m³

Word Problem 9 (Application-Based)

A wall is 15 m long and 4 m high. Painting costs ₹35 per square metre.

Find the total painting cost.

Solution

Area = 15 × 4

= 60 m²

Cost = 60 × 35

= ₹2,100

Answer: ₹2,100

Word Problem 10 (HOTS)

The perimeter of a square is 72 cm. Find its area.

Solution

Side = 72 ÷ 4

= 18 cm

Area = 18²

= 324 cm²

Answer: 324 cm²

Fill in the Blanks

The boundary length of a figure is called Perimeter.
Area is measured in square units.
Volume is measured in cubic units.
Area of a rectangle = Length × Breadth.
Area of a triangle = ½ × Base × Height.
Compute circle area = πr².
Circumference of a circle = 2πr.
Volume of a cube = a³.
Volume of a cuboid = l × b × h.
TSA of a cube = 6a².

True or False

Area is measured in cm³. → False
Volume is measured in cubic units. → True
Perimeter means boundary length. → True
Area of a square = 4 × Side. → False
Area of a rectangle = Length × Breadth. → True
Surface area is measured in square units. → True
Cube has 6 faces. → True
Cuboid has 8 vertices. → True
Circle has four sides. → False
Radius is half of the diameter. → True

Match the Following

Column A	Column B
Square	a²
Rectangle	l × b
Triangle	½bh
Circle	πr²
Cube	a³
Cuboid	l × b × h
Cylinder	πr²h
Boundary	Perimeter
Inside Region	Area
Space Occupied	Volume

Very Short Answer Questions (1 Mark)

Q1. What is Mensuration?

Answer: Mensuration is the branch of mathematics that deals with the measurement of geometrical figures and solids.

Q2. Define Perimeter.

Answer: The total length of the boundary of a closed figure is called its perimeter.

Q3. Define Area.

Answer: The region enclosed inside a closed figure is called its area.

Q4. What is Volume?

Answer: Volume is the space occupied by a three-dimensional object.

Q5. Write the SI unit of Area.

Answer: Square metre (m²).

Short Answer Questions (2–3 Marks)

Q1. Differentiate between Area and Perimeter.

Area	Perimeter
Measures enclosed region	Measures boundary length
Square units	Linear units

Q2. Write any four applications of Mensuration.

Answer:

Construction of buildings
Painting walls
Agriculture
Flooring and tiling

Q3. Why is Volume measured in cubic units?

Answer: Because volume depends on length, breadth, and height, which are multiplied together.

Q4. Write the formulas for the following:

Area of Square, Rectangle, Triangle and Circle ?

Long Answer Questions (5 Marks)

Q1. Explain the importance of Mensuration in daily life.

Answer

Mensuration is useful in many real-life situations such as:

House construction
Road construction
Painting and polishing
Agriculture
Water storage
Interior decoration
Packaging
Architecture
Engineering
Sports ground design

Q2. Explain the difference between Surface Area and Volume with examples.

Surface Area	Volume
Outer surface	Space occupied
Square units	Cubic units
Used for painting	Used for storage

Example:

Painting a wall → Surface Area
Filling a water tank → Volume

Practice Worksheet (20 Marks)

Section A (1 Mark Each)

Calculate the perimeter of a square of side 12 cm.
Determine the area of a rectangle of dimensions 8 cm × 6 cm.
Compute the area of a triangle with base 10 cm and height 8 cm.
Evaluate the circumference of a circle of radius 7 cm.
Find the volume of a cube of side 5 cm.

Section B (2 Marks Each)

Compute the area of a trapezium with parallel sides 18 cm and 12 cm, and height 8 cm.
Evaluate the total surface area of a cube with side 6 cm.
Find the volume of a cuboid measuring 10 cm × 6 cm × 4 cm.

Section C (3 Marks Each)

A rectangular garden is 25 m long and 18 m wide. Find:

(a) Perimeter
(b) Area

A cylindrical tank has radius 7 m and height 8 m. Find its volume.

Answer Key

48 cm
48 cm²
40 cm²
44 cm
125 cm³
120 cm²
216 cm²
240 cm³
Perimeter = 86 m, Area = 450 m²
1232 m³

Exam Tips

Read the question carefully.

Draw the figure if needed.

Write the correct formula before solving.

Show all calculation steps.

Mention the correct units in the final answer.

Recheck your calculations.

Quick Revision Box

Perimeter → Boundary Length

Area → Enclosed Region

Surface Area → Outer Covering

Volume → Space Occupied

Area Unit → cm², m²

Volume Unit → cm³, m³

Perimeter Unit → cm, m

NCERT Exercise 9.1 (Area of Trapezium and General Quadrilateral)

Important Formula

Area of Trapezium

Area = ½ × (Sum of Parallel Sides) × Height

हिंदी

क्षेत्रफल = ½ × (समांतर भुजाओं का योग) × ऊँचाई

Solved Question 1

Question

The parallel sides of a trapezium are 18 cm and 12 cm. Height is 8 cm.

Find its area.

Solution

Area

= ½ × (18 + 12) × 8

= 120 cm²

Answer: 120 cm²

Solved Question 2

The parallel sides are 20 cm and 14 cm.

Height = 10 cm

Area

= ½ × (20 + 14) × 10

= 170 cm²

Exam Tip

✔ Always add the parallel sides first, then multiply by the height.

NCERT Exercise 9.2 (Surface Area)

Formula Sheet

Cube

TSA = 6a²

LSA = 4a²

Cuboid

TSA = 2(lb + bh + hl)

LSA = 2h(l + b)

Cylinder

CSA = 2πrh

TSA = 2πr(r + h)

Solved Question 1

A cube has side 8 cm.

Find Total Surface Area.

Solution

TSA

= 6 × 8²

= 384 cm²

Solved Question 2

A cuboid measures

Length = 12 cm

Breadth = 8 cm

Height = 6 cm

Find TSA.

Solution

= 2(lb + bh + hl)

= 432 cm²

Solved Question 3

Radius = 7 cm

Height = 10 cm

Find Curved Surface Area.

Solution

CSA

= 2πrh

= 440 cm²

Solved Question 4

Find TSA of the above cylinder.

TSA

= 2πr(r+h)

= 748 cm²

NCERT Exercise 9.3 (Volume)

Formula Chart

Cube

Volume = a³

Cuboid

Volume = l × b × h

Cylinder

Volume = πr²h

Solved Question 1

Cube side = 9 cm

Volume

= 9³

= 729 cm³

Solved Question 2

Cuboid

Length = 15 cm

Breadth = 8 cm

Height = 6 cm

Volume

= 15 × 8 × 6

= 720 cm³

Solved Question 3

Cylinder

Radius = 7 cm

Height = 12 cm

Volume

= 22/7 × 7 × 7 × 12

= 1848 cm³

NCERT Important Questions

Question 1

Find the area of a trapezium having

Parallel sides

16 cm and 10 cm

Height = 8 cm

Solution

Area

= ½ × (16 + 10) × 8

= 104 cm²

Question 2

Find the TSA of a cube of side 5 cm.

Solution

= 6 × 25

= 150 cm²

Question 3

Find the volume of a cuboid

10 × 8 × 5

Solution

= 400 cm³

Question 4

Find the volume of a cylinder

Radius = 14 cm

Height = 8 cm

Solution

= 22/7 × 14 × 14 × 8

= 4928 cm³

Previous Year NCERT-Based Questions

Find the area of a trapezium whose parallel sides are 24 cm and 16 cm, and height is 10 cm.

Answer: 200 cm²

Find the total surface area of a cube having side 12 cm.

Answer: 864 cm²

Find the volume of a cube of side 15 cm.

Answer: 3375 cm³

A cuboid measures 20 cm × 12 cm × 10 cm.

Find its volume.

Answer: 2400 cm³

Find the curved surface area of a cylinder having radius 14 cm and height 15 cm.

Answer: 1320 cm²

Common Mistakes in NCERT Exercises

Forgetting to convert units.

Writing cm² instead of cm³ for volume.

Using the perimeter formula instead of the area formula.

Forgetting to divide by 2 in the trapezium area formula.

Confusing CSA with TSA.

Using an incorrect value of π.

NCERT Exam Tips

Write the formula first.

Substitute values carefully.

Show every calculation step.

Draw diagrams where possible.

Mention the correct unit in the final answer.

Recheck calculations before submission.

Quick Revision Table

Figure	Formula
Square	Area = a²
Rectangle	Area = l × b
Triangle	Area = ½bh
Trapezium	Area = ½(a+b)h
Circle	Area = πr²
Cube	Volume = a³
Cuboid	Volume = lbh
Cylinder	Volume = πr²h

Practice Questions

Find the area of a trapezium with parallel sides 25 cm and 15 cm, and height 12 cm.
Compute the TSA of a cube of side 14 cm.
Compute the volume of a cuboid measuring 16 cm × 10 cm × 8 cm.
Find the volume of a cylinder having radius 7 cm and height 20 cm.
Find the CSA of a cylinder with radius 10 cm and height 14 cm.

Answer Key

240 cm²
1176 cm²
1280 cm³
3080 cm³
880 cm²

Frequently Asked Questions (FAQs)

PART 1

Q1. What is Mensuration?

English: Mensuration is the branch of mathematics that deals with the measurement of geometrical figures and solid objects.

Hindi: Mensuration गणित की वह शाखा है जिसमें समतल आकृतियों (2D) और ठोस आकृतियों (3D) का मापन किया जाता है।

Q2. What is the difference between Perimeter and Area?

Answer:

Perimeter	Area
Total boundary length	Region enclosed inside a figure
Linear units	Square units

Q3. Why is Area measured in square units?

Answer:

Area is obtained by multiplying length × breadth, so its unit becomes square units (cm², m²).

Q4. Why is Volume measured in cubic units?

Answer:

Volume is calculated by multiplying length × breadth × height, so it is measured in cubic units (cm³, m³).

Q5. What is the SI unit of Area?

Answer: Square metre (m²).

Q6. What is the SI unit of Volume?

Answer: Cubic metre (m³).

Q7. What is the formula for the Area of a Rectangle?

Answer:

Area = Length × Breadth

Q8. What is the formula for the Area of a Triangle?

Answer:

Area = ½ × Base × Height

Q9. What is the formula for the Area of a Circle?

Answer:

Area = πr²

PART 2

Q10. What is the formula for the Circumference of a Circle?

Answer:

Circumference = 2πr

Q11. What is the formula for the Volume of a Cube?

Answer:

Volume = a³

Q12. What is the formula for the Volume of a Cuboid?

Answer:

Volume = l × b × h

Q13. What is the formula for the Volume of a Cylinder?

Answer:

Volume = πr²h

Q14. What is Total Surface Area (TSA)?

Answer:

The total area covering all the outer surfaces of a solid object is called its Total Surface Area (TSA).

Q15. What is Curved Surface Area (CSA)?

Answer:

The area of only the curved portion of a solid object is called Curved Surface Area (CSA).

Q16. What is the difference between TSA and CSA?

TSA	CSA
Includes all surfaces	Includes only the curved surface
Example: Cylinder with top and bottom	Cylinder without top and bottom

Q17. Which value of π should be used in Class 8?

Answer:

Use 22/7 unless the question specifies 3.14.

Q18. Why should units be converted before solving?

Answer:

All measurements must be in the same unit to ensure the correct answer.

Q19. Where is Mensuration used in daily life?

Answer:

Construction
Agriculture
Painting
Interior Design
Packaging
Engineering
Architecture
Sports Ground Design
Water Storage
Flooring

Q20. Which topics are most important for exams?

Answer:

Perimeter
Area
Surface Area
Volume
Unit Conversion
Formula Application
Word Problems

Viva Questions (Oral Test)

Q1. What is Mensuration?

Answer: Measurement of geometrical figures.

Q2. Define Area.

Answer: Area is the region enclosed inside a figure.

Q3. Define Perimeter.

Answer: Perimeter is the total length of the boundary.

Q4. Define Volume.

Answer: Volume is the space occupied by a solid.

Q5. Which unit is used for Area?

Answer: Square units.

Q6. Which unit is used for Volume?

Answer: Cubic units.

Q7. Name any two three-dimensional shapes.

Answer:

Cube
Cuboid

Q8. Name any two plane figures.

Answer:

Square
Rectangle

Q9. What is the value of π?

Answer: 22/7 or 3.14

Q10. Which quantity is used for fencing?

Answer: Perimeter

One-Page Revision Notes

Important Formulas

Square

Perimeter = 4a

Area = a²

Rectangle

Perimeter = 2(l+b)

Area = l × b

Triangle

Area = ½bh

Trapezium

Area = ½(a+b)h

Circle

Circumference = 2πr

Area = πr²

Cube

TSA = 6a²

Volume = a³

Cuboid

TSA = 2(lb+bh+hl)

Volume = lbh

Cylinder

CSA = 2πrh

TSA = 2πr(r+h)

Volume = πr²h

Last-Minute Revision Tips

Learn all formulas.

Practice numerical questions daily.

Revise unit conversions.

Solve previous year questions

Write formulas before calculations.

Draw figures where needed.

Revise mistakes from your notebook.

Practice at least 10 word problems.

10 Most Important Questions for Exams

Calculate the area of a trapezium.
Determine the perimeter of a rectangle.
Evaluate the area of a circle.
Compute the total surface area (TSA) of a cube.
Work out the volume of a cuboid.
Calculate the curved surface area (CSA) of a cylinder.
Determine the volume of a cylinder.
Convert square metres (m²) into square centimetres (cm²).
Differentiate between Area and Perimeter with suitable examples.
Describe the practical applications of Mensuration in daily life.

Common Student Doubts

Doubt 1

Should I write units?

Yes. Answers without units may lose marks.

Doubt 2

Can I use 3.14 instead of 22/7?

Only if the question allows it.

Doubt 3

Should diagrams be drawn?

Yes, wherever possible.

Doubt 4

Should formulas be written?

Always write the formula before solving.

Doubt 5

Can I skip steps?

No. Stepwise solutions help in getting partial marks even if the final answer is incorrect.

Key Takeaways

Mensuration deals with the measurement of geometrical figures.
Perimeter measures the boundary, while Area measures the enclosed region.
Surface Area measures the outer covering of a solid.
Volume measures the space occupied by a solid.
Correct formulas and units are essential for scoring full marks.
Regular practice of NCERT exercises, MCQs, and word problems improves accuracy and speed.

Conclusion

Understanding Mensuration is essential for every Class 8 student because it builds a strong foundation for higher mathematics and real-life applications. By mastering concepts such as Perimeter, Area, Surface Area, and Volume, students can solve practical problems related to construction, architecture, engineering, agriculture, and daily life with confidence.

This comprehensive guide covered all important concepts, formulas, solved examples, MCQs, HOTS questions, word problems, revision notes, and exam-oriented practice questions in both English and Hindi. Regular practice of these questions and formulas will improve speed, accuracy, and confidence in examinations.

If you found these Mensuration Class 8 Notes helpful, bookmark this page and share it with your friends. Keep visiting www.risingstarmindset.com for more CBSE Notes, NCERT Solutions, MCQs, PYQs, and study materials.

निष्कर्ष (Hindi)

Mensuration (मापन) गणित का एक अत्यंत महत्वपूर्ण अध्याय है जो विद्यार्थियों को वास्तविक जीवन की समस्याओं को हल करने में सक्षम बनाता है। यदि आप Perimeter, Area, Surface Area और Volume के सूत्रों और उनके उपयोग को अच्छी तरह समझ लेते हैं, तो स्कूल परीक्षाओं के साथ-साथ प्रतियोगी परीक्षाओं में भी अच्छे अंक प्राप्त कर सकते हैं।

इस लेख में हमने सिद्धांत, सूत्र, उदाहरण, MCQs, HOTS, Word Problems, Revision Notes और परीक्षा की दृष्टि से महत्वपूर्ण प्रश्नों का विस्तृत अध्ययन किया। नियमित अभ्यास और सूत्रों का पुनरावृत्ति (Revision) सफलता की कुंजी है।

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