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:

$A=\dfrac{1}{2}r^2\theta$

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

$15\pi=\dfrac{1}{2}(5)^2\theta$

Multiply both sides by 2.

$30\pi=25\theta$

Divide both sides by 25.

$\dfrac{30\pi}{25}=\theta$

$\dfrac{6\pi}{5}=\theta$

Therefore, the central angle in radians is $\theta=\dfrac{6\pi}{5}$.