Chapter 20 · ICSE Class 7 Mathematics

Mensuration

Measure circles, parallelograms, and 3D solids — finding circumference, area, and volume with the right formulas.

📐 Chapter 20

A circle with its radius labeled and circumference formula shown A circle with a radius line labeled r, and the circumference formula 2 pi r shown below r Circumference = 2πr
20.1

Circumference and Area of a Circle

A circle's circumference (perimeter) is found using C = 2πr, and its area using A = πr², where r is the radius. Using π ≈ 22/7 or 3.14 makes calculations practical.

1

Find the circumference of a circle with radius 7cm. (Use π = 22/7)

2 × 22/7 × 7 = 44cm

2

Find the area of a circle with radius 14cm. (Use π = 22/7)

22/7 × 14 × 14 = 616 square cm

20.2

Volume and Surface Area of Cubes and Cuboids

For a cuboid: Volume = length × width × height, and Total Surface Area = 2(lw + wh + lh). For a cube, where all sides are equal: Volume = side³, and Total Surface Area = 6 × side².

1

Find the volume of a cuboid 8cm × 5cm × 4cm.

8 × 5 × 4 = 160 cubic cm

2

Find the volume of a cube with side 6cm.

6³ = 216 cubic cm

Practice

Exercises

1. Find the circumference of a circle with radius 21cm. (Use π = 22/7)

2. Find the area of a circle with radius 7cm. (Use π = 22/7)

3. Find the volume of a cuboid 10cm × 6cm × 5cm.

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

5. A cuboid water tank is 2m long, 1.5m wide, and 1m high. Find its volume in cubic meters.