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