Question

Question 99

Find the area of the shaded region:

Answer 1

$\because$ Diameter of complete circle = 14 cm
$\therefore$ Radius $=\frac{14}{2}=7cm[\because radius=\frac{diameter}{2}]$
So, area of complete circle $=\pi r^2=\frac{22}{7}\times 7\times 7=154c{m}^2$
$\because$ Diameter of small circle $=\frac{7}{4}cm$
$\therefore$ Radius $=\frac{7}{4\times 2}=\frac{7}{8}cm$
$\therefore$ Area of two small circles $=2\times \pi r^2=2\times \frac{22}{7}\times \frac{7}{8}\times \frac{7}{8}=\frac{77}{16}c{m}^2$
$\therefore$ Area of shaded region = Area of complete circle - Area of two small circles
$=154-\frac{77}{16}=\frac{154\times 16-77}{16}$ [taking LCM]
$=\frac{2464-77}{16}=\frac{2387}{16}=149\frac{3}{16}c{m}^2$
Hence, the area of shaded region is $149\frac{3}{16}c{m}^2.$