Question

If the area of the shaded part is $\frac{72}{7}sq.$ units then find the radius of the circle.

Answer 1

Area of shaded part = Area of circle - Area of square

$\frac{72}{7}=\pi r^2-A^2...\left(1\right)$

$△$ QSR, using Pythagoras therm

$2A^2=(2r{)}^2$

$2A^2=4r^2$

$A=\sqrt{2r}$...(2)

by eq(1)& eq(2)

$\frac{72}{7}=\pi r^2-2r^2$

$\frac{72}{7}=(\frac{22}{7}-1{)}^{r^2}$

$\frac{72}{7}=\frac{15}{7}{r}^2=\frac{72}{15}\Rightarrow \sqrt{\frac{72}{15}}$

$r=2.1908$