Question

Two small circles touching each other externally and of radius 6 cm are inscribed in a circle. Find the shaded area. [Take π = 3.14]

Answer 1

Given:

• Two small circles touch each other externally.
• Each small circle has radius 6 cm.
• Both are inscribed in a larger circle, meaning all three centers lie on a straight line and the outer circle encloses both.

Step 1: Find diameter of the larger circle

Since the smaller circles touch each other externally, the distance between their centers is:

6 cm + 6 cm = 12 cm

This segment is part of the diameter of the larger circle.

Add one radius on each side:

Diameter of larger circle = 6 + 12 + 6 = 24 cm

Radius of larger circle = `24/2` = 12 cm

Step 2: Area of the larger circle

A = πr²

= 3.14 × 12²

= 3.14 × 144

= 452.16 cm²

Step 3: Area of each small circle

A = πr²

= 3.14 × 6²

= 3.14 × 36

= 113.04 cm²

There are two such circles:

2 × 113.04 = 226.08 cm²

Step 4: Shaded area

Shaded area = Area of larger circle – Area of 2 smaller circles

= 452.16 – 226.08

= 226.08 cm²