Question

if the area of a sector is 15pi square cm and the radius is 5cm find the measure of the central angle​

Answer 1

Given:

Area of a sector =
`15\pi`

Radius = 5 cm

To find:

The central angle.

Solution:

The area of a sector is:

`A=(1)/(2)r^2\theta`

Where, r is the radius and
`\theta` is the central angle in radians.

Putting
`A=15\pi, r=5` in the above formula, we get

`15\pi=(1)/(2)(5)^2\theta`

Multiply both sides by 2.

`30\pi=25\theta`

Divide both sides by 25.

`(30\pi)/(25)=\theta`

`(6\pi)/(5)=\theta`

Therefore, the central angle in radians is
`\theta=(6\pi)/(5)`.