Question

A sector with an area of 48\pi cm^(2) has a radius of 16 cm. what is the central angle measure of the sector in radians

Answer 1

Answer:

The central angle is = 3/8  π

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, 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

$\frac{48}{128}$ π  =   Ф

Ф  =  $\frac{48}{128}$ π

The right-hand side can be reduced to its lowest term

Ф =  48 ÷  16   /    128  ÷16   π

Ф = 3/8  π