Question

Four equal circle are described at the four concern of the square so that each touches two of the other. The should area enclosed between the circle is 24 cm. Find the radius of each area and side of square.

Answer 1

Given area of shaded region$=24c{m}^2$

$\Rightarrow 4\left[\frac{1}{4}\pi r^2\right]=24c{m}^2$

$\Rightarrow r^2=\frac{24}{\pi }c{m}^2$

$\therefore$ Area of the square $=(2r{)}^2=4r^2$

Area of square $=\frac{96}{{\pi }^2}c{m}^2$

Side of square $2r=\frac{48}{\pi }$

Radius of each circle $=r\sqrt{\frac{24}{\pi }}$cm.