Question

In the figure, two small circles touch each other externally at the centre of a bigger circle and these small circles are touched internally by a bigger circle with radius 4 $cm$. Find the area of the shaded region in $c{m}^2$.

• A. 27.52
• B. 30.73
• C. 100.48
• D. 78.64

Answer 1

The correct option is A

27.52

From the figure, two circles of radius 4 cm exist in the rectangle.

Their total area = 2$\pi r^2$ = 2 $\times$ 3.14 x 16 = 100.48 $c{m}^2$

From figure
Length of rectangle is 4r = 16 cm
Breadth of rectangle is 2r = 8 cm

Area of rectangle = 16 x 8 = 128 $c{m}^2$

Required area = [Area of rectangle - Total area of circles]
= 128 - 100.48 = 27.52 $c{m}^2$.

$\therefore$ The area of the shaded region
= 27.52 $c{m}^2$.