# How do you find the radius of each circle if the area of the sector is 28 and the angle is 150 degrees?

Nov 7, 2015

radius $\cong 4.625$

#### Explanation:

If a sector of ${150}^{\circ}$ has an area of $28$

then a sector of ${1}^{\circ}$ has an area of $\frac{28}{150}$ = 0.186667#

and a full circle, which is a sector of ${360}^{\circ}$ has an area of $0.186667 \times 360 = 67.200$

The area of a circle is $\pi {r}^{2}$

so $\pi {r}^{2} = 67.200$
and
$\textcolor{w h i t e}{\text{XXX}} {r}^{2} = \frac{67.200}{\pi} = 21.39042$

and
$\textcolor{w h i t e}{\text{XXX}} r = \sqrt{21.39042} \cong 4.625$