Question

The area of a circle is equal to the sum of the areas of 3 circles of radii 2 cm, 3 cm and 6 cm. Find the radius and the circumference of the new circle formed.

Answer 1

Given: The area of a new circle is equal to the sum of the areas of three circles with radii 2 cm, 3 cm and 6 cm.

Step-wise Calculation:

1. Area of a circle = πr²

2. Area of three given circles:

π × 2² + π × 3² + π × 6²

= π(4 + 9 + 36)

= π × 49

3. Let the radius of the new circle be R. 

Then, area of the new circle = πR².

4. Since the area of the new circle is equal to the sum of areas of the three circles πR² = π × 49

5. Dividing both sides by π: R² = 49

6. Taking the square root: R = 7 cm

7. Circumference of a circle = 2πR

= `2 xx 22/7 xx 7`

= 44 cm 

Radius of the new circle formed is 7 cm.

Circumference of the new circle is 44 cm.