Question

The area of the ring between two concentric circles, whose circumference are $88cm$ and $132cm$, is:

• A. $780{cm}^2$
• B. $770{cm}^2$
• C. $715{cm}^2$
• D. $660{cm}^2$

Answer 1

The correct option is B $770{cm}^2$

Circumference of Bigger circle $=132cm$

$2\pi R=132$

$2\times \frac{22}{7}\times R=132$

$R=\frac{132\times 7}{2\times 22}$

$R=21cm$

Circumference of Smaller circle $=88cm$

$2\pi r=88$

$2\times \frac{22}{7}\times r=88$

$r=\frac{88\times 7}{2\times 22}$

$r=44cm$

Area of the ring $=$ Area of bigger circle $-$ Area of smaller circle

$=\pi R^2-\pi r^2$

$=\pi (R^2-r^2$

$=\frac{22}{7}({21}^2-{14}^2$

$=\frac{22}{7}\times 245$

$=770c{m}^2$