Question

$AC$ and $BD$ are two perpendicular diameters of circle $ABCD$. Given that, the area of the shaded portion is $308c{m}^2$. Calculate (i) the length of $AC$ and (ii) the circumference of the circle.

Answer 1

Area of sector $(OAB+OCD)=2\times \frac{\pi r^2}{4}...$ (angle $=\frac{\pi }{2}$)

$\therefore \frac{\pi r^2}{2}=308c{m}^2$

$\therefore \frac{22r^2}{7\times 2}=308c{m}^2$

$\therefore r^2=\frac{308\times 7}{11}$

$\therefore r^2=196={14}^2$

$\therefore r=14cm$

$\therefore$ length $l\left(AC\right)=2r=2\times 14=28cm$

$\therefore$ Circumference $=2\pi r$

$=2\pi \left(14\right)$

$=28\pi cm$