Question

ABCD is a flower bed. If $OA=21cm$ and $OC=14m$, find the area of the bed. [Use $\pi =\frac{22}{7}$]

• A. $161.4m^2$
• B. $192.5m^2$
• C. $212.6m^2$
• D. $\mathrm{257.2.5}{m}^2$

Answer 1

The correct option is B $192.5m^2$

We have,
$OA=R=21m$ and $OC=r=14m$
$\therefore$ Area of the flower bed
=Area of a quadrant of a circle of radius R - Area of a quadrant of a circle of radius r
$=\frac{1}{4}\pi R^2-\frac{1}{4}\pi r^2$
$=\frac{\pi }{4}(R^2-r^2)$
$=\frac{1}{4}\times \frac{22}{7}({21}^2-{14}^2)c{m}^2$ $[\therefore R=12m$ and $r=14m]$
$=(\frac{1}{4}\times \frac{22}{7}\times (21+14\left)\right(21-14\left)\right)m^2$
$=(\frac{1}{4}\times \frac{22}{7}\times 35\times 7)m^2=192.5m^2$