Question

An arc of a circle is of length $7\pi cm$ and the sector it bounds has an area of $28\pi c{m}^2$. Find the radius of the circle.

Answer 1

Arc of circle of length $=7\pi cm.$

Sector it bounds has an area $=28\pi c{m}^2.$

Radius of circle $=?$

We know that.

Length of an arc of circle $\frac{2\pi r\theta }{{360}^0}$

Therefore,

$\frac{2\pi r\theta }{{360}^0}$ $=$ $7\pi$

$r\theta ={180}^0\times 7$

$\theta =\frac{1260}{r}......\left(1\right)$

And

Area of the sector= $\frac{\pi r^2\theta }{{360}^0}$

$\frac{\pi r^2\theta }{{360}^0}$$=$ $28\pi$

$r^2\theta =28\times {360}^0$

$\theta =\frac{28\times {360}^0}{r^2}......\left(2\right)$

From (1) and (2) to and we get,

$\frac{1260}{r}=\frac{28\times {360}^0}{r^2}$

$r=\frac{28\times {360}^0}{1260}$

$r=8c.m$

Hence, this is the answer.