Question

A square is inscribed in a circle. If the area of the shaded region is $224$ $c{m}^2$, calculate the radius.

Answer 1

Let the radius of the circle be $r$

Area of shaded region = Area of circle - Area of square

Area of the circle $=\pi r^2$

length of diagonal of square $=2r$

side of square $=\sqrt{2}r$

area of square $=2r^2$

$\pi r^2-2r^2=224$

$(\frac{22}{7}-2)r^2=224$

$\frac{8}{7}{r}^2=224$

$r^2=196$

$r=14cm$

The radius of circle is $14cm$