Answer:
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