Question

What is the radius of the sector?

Answer 1

5 units

Explanation:

The area of a sector is
`A=(r^2\theta)/(2)` where
`r` is the radius and
`\theta` is the angle formed:

`A=(r^2\theta)/(2)\\\\(75\pi)/(16) =(r^2((3\pi)/(8)))/(2)\\\\150\pi=16r^2((3\pi)/(8))\\\\150\pi=6\pi r^2\\\\25=r^2\\\\5=r`

Therefore, the radius of the sector is 5 units