Question

The area between two concentric circles is 1078 cm². The circumference of the inner circle is 132 cm. Find the width of the ring.

Answer 1

Given:

• Area between two concentric circles = 1078 cm²
• Circumference of the inner circle = 132 cm

Stepwise calculation:

1. Let the radius of the inner circle be (r). 

Using the circumference formula:

2πr = 132

Taking `π = 22/7`, 

`2 xx 22/7 xx r = 132`

`r = (132 xx 7)/(2 xx 22)`

r = 21 cm

2. Let the radius of the outer circle be (R).

The area between two concentric circles the ring area is given by: 

π(R² – r²) = 1078

Substitute `π = 22/7` and r = 21: 

`22/7 (R^2 - 21^2) = 1078`

`R^2 - 441 = (1078 xx 7)/22`

`R^2 - 441 = 343`

`R^2 = 441 + 343 = 784`

`R = sqrt(784)`

R = 28 cm

3. Width of the ring = Difference between outer and inner radius: 

R – r 

= 28 – 21

= 7 cm

The width of the ring is 7 cm.