Question

The area of the black region is $100(\pi -2)unit{s}^2$. Calculate the diameter of the circle.

Answer 1

Area of black $=$(Area of circle) $-$ (Area of square)

$100(\pi -2)=\pi r^2-a^2$ …………$\left(1\right)$

Diameter of the circle $=2r=$ diagonal of the square

$AC=\sqrt{2}$

$\therefore 2r=\sqrt{2}a$

$\therefore a=\frac{2}{\sqrt{2}}r$

$=\sqrt{2}r$

$100(\pi -2)=\pi r^2=(\sqrt{2}r\times \sqrt{2}r)=\pi r^2-2r^2$

$100(\pi -2)=r^2(\pi -2)$

$\therefore r^2=100$

$\therefore r=10$ units

$\therefore$ Diameter $=2r=2\times 10=20$ units.