Question

The given figure consists of a square, a quarter circle and a semicircle.

Area of a sector is πr2θ360∘ All the sides of a square are equal. Find the area of the shaded portion.

• A. $\frac{25}{2}sq.units$
• B. $25\pi sq.units$
• C. $\frac{25\pi }{2}sq.units$
• D. $\frac{25\pi }{4}sq.units$

Answer 1

The correct option is C $\frac{25\pi }{2}sq.units$

Area of shaded part $=$ Area of quarter circle $-$ Area of semi-circle

$=\frac{1}{4}\pi r^2-\frac{1}{2}\pi r^2$

$=\frac{1}{4}\times \pi \times 10\times 10-\frac{1}{2}\times \pi \times 5\times 5$

$=25\pi -\frac{25\pi }{2}$

$=\frac{25\pi }{2}$ sq.units