Question

What is the radius of a sector

Answer 1

Answer:

$\frac{10}{3}$ units

Step-by-step explanation:

Recall that the area of a sector is $A=\frac{r^2\theta}{2}$ where $r$ is the radius and $\theta$ is the angle of the sector (measured in radians).

Therefore, the radius of the sector is:

$A=\frac{r^2\theta}{2}$

$\frac{100\pi}{27}=\frac{r^2(\frac{2\pi}{3})}{2}$

$200\pi=27r^2(\frac{2\pi}{3})$

$200\pi=r^2(\frac{54\pi}{3})$

$200\pi=r^2(18\pi)$

$\frac{200}{18}=r^2$

$\frac{100}{9}=r^2$

$\frac{10}{3}=r$

So, the radius of the sector is $\frac{10}{3}$ units.