Question

The radius of a circle is 7 cm and it forms a sector by rotating through 60${}^{\circ }$. Then, the radius gets doubled and further moves 30${}^{\circ }$ to form another sector. What is the area of the total region covered by the radius? ( Take π= $\frac{22}{7}$)

• A. 308 $c{m}^2$
• B. 154 $c{m}^2$
• C. 77 $c{m}^2$
• D. 144 $c{m}^2$

Answer 1

The correct option is C

77 $c{m}^2$

Area of the sector until the radius is doubled = Area of the pink part

= $\frac{60}{360}\times \pi \times r^2$ = $\frac{\pi \times r^2}{6}$
$=\frac{22}{7}\times 7\times 7\times \frac{1}{6}$
$=\frac{154}{6}c{m}^2$ ------(1)

Area of the sector made by the doubled radius = Area of orange part

= $\frac{22}{7}\times \frac{30}{360}\times \left(\right(2r{)}^2)$
$=\frac{22}{7}\times 14\times 14\times \frac{1}{12}$
$=\frac{616}{12}c{m}^2$ ------(2)

Adding (1) and (2) we get

The total area covered by the radius $=\frac{154}{6}+\frac{616}{12}$
$=\frac{924}{12}=77c{m}^2$