Answer:
The central angle is = 3/8 π
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, since we are asked to find the central angle measure of the sector in radians, then we will use the second formula
area = 48π cm² and radius = 16 cm
area of sector = 1/2 × r² × Ф
48π = 1/2 × 16² × Ф
48π = 1/2 ×256 × Ф
48π = 128×Ф
Divide both-side of the equation by 128
π = Ф
Ф =
π
The right-hand side can be reduced to its lowest term
Ф = 48 ÷ 16 / 128 ÷16 π
Ф = 3/8 π