A sector with a radius of 15 cm has a central angle measure of 8π/5 what is the area of the sector

area of the sector = 360π cm²

Step-by-step explanation:

To calculate the area of the sector, we will follow the steps below;

First write down the formula for calculating the area of a sector.

If angle Ф is measured in degree, then

area of sector = Ф/360 * πr²

but if angle Ф is measured in radians, then

area of sector = 1/2 * r² * Ф

In this case the angle is measured in radiance, hence we will use the second formula

From the question given, radius = 15 cm and angle Ф = 8π/5

area of sector = 1/2 * r² * Ф

=1/2 * 15² * 8π/5

=1/2 * 225 * 8π/5

=360π cm²

area of the sector = 360π cm²