Question

In the following figure, the area enclosed between the concentric circles is 770 cm². Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle `(π = 22/7)`.

Answer 1

Given: Area of the region between the concentric circles = 770 cm²; outer radius R = 21 cm; π = `22/7`.

Step-wise calculation:

1. Area of annulus

= π(R² – r²)

= 770

2. Substitute values:

`22/7 (21^2 - r^2) = 770`

3. 21² = 441

So, `22/7 (441 - r^2) = 770`.

4. Multiply both sides by 7:

22(441 – r²)

= 770 × 7 

= 5390

5. Divide by 11 (since 22 = 2 × 11):

2(441 – r²) = 490

6. So, 441 – r² = 245

⇒ r² = 441 – 245

= 196

7. r = `sqrt(196)`

= 14 cm

The radius of the inner circle is 14 cm.