Question

The area of the shaded portion in the given figure is

• A. 7.5 $\pi$ sq. units
• B. 6.5 $\pi$ sq. units
• C. 5.5 $\pi$ sq. units
• D. 4.5 $\pi$ sq. units

Answer 1

The correct option is D 4.5 $\pi$ sq. units

Area of the outer semi-circle $=\frac{\pi }{2}\times 5^2$
Area of the inner semi-circle $=\frac{\pi }{2}\times 4^2$
$\therefore$ Area of shaded region $=$ Area of outer semicircle- Area of inner semicircle$=\frac{\pi }{2}\times 5^2-\frac{\pi }{2}\times 4^2$
$=\frac{\pi }{2}(25-16)$
$=4.5\pi c{m}^2$