Question

Circumference of inner and outer circle of a ring are 44 cm and 132 cm respectively, then find the area of the ring.

• A. 392 $c{m}^2$
• B. 441 $c{m}^2$
• C. 576 $c{m}^2$
• D. 1232 $c{m}^2$

Answer 1

The correct option is D 1232 $c{m}^2$

Circumference = 2$\pi$r
for inner circle
r = $\frac{Circumference}{2\pi }$ = $\frac{44}{2\pi }$ = $\frac{44\times 7}{2\times 22}$ = 7 cm

Similarly
for outer circle
R = $\frac{Circumference}{2\pi }$ = $\frac{132}{2\pi }$ = $\frac{132\times 7}{2\times 22}$ = 21 cm

Area of ring = $\pi$($R^2$ - $r^2$)
= $\frac{22}{7}$$\times$(${21}^2$ - $7^2$)
= $\frac{22}{7}$$\times$(441 - 49)
= $\frac{22}{7}$$\times$392
= 22$\times$56 = 1232