Question

What is the radius of the sector?

Answer 1

Answer:

5 units

Step-by-step explanation:

The area of a sector is $A=\frac{r^2\theta}{2}$ where $r$ is the radius and $\theta$ is the angle formed:

$A=\frac{r^2\theta}{2}\\\\\frac{75\pi}{16} =\frac{r^2(\frac{3\pi}{8})}{2}\\\\150\pi=16r^2(\frac{3\pi}{8})\\\\150\pi=6\pi r^2\\\\25=r^2\\\\5=r$

Therefore, the radius of the sector is 5 units