Question

A circle has a radius of 5 inches (What is the measure, in radians, of this central angle?

Answer 1

Explanation:

Given

Circle has radius
`r=5 in.`

Area of the sector is given by

`A_s=(\theta )/(2\pi )* \pi r^2`

if
`A_s` is one-sixth of area of circle then

`A_s=(\pi r^2)/(6)`

`(\pi r^2)/(6)=(\theta )/(2\pi )* \pi r^2`

`\theta =(2\pi )/(6)=(\pi )/(3)\ radian`

If
`A_s` is one-fourth of area of circle then

`A_s=(\pi r^2)/(4)`

`\theta =(2\pi )/(4)`

`\theta =(\pi )/(2)`