Question

A sector with an area of 48 pi cm2 has a radius of 16 cm.

What is the central angle measure of the sector in radians?

Answer 1

The central angle is 3π/8 rad

Explanation:

Area of a sector is expressed as
`(\theta)/(360^(0) ) *\pi r^(2)`

r is the radius of the circle

`\theta` is the angle substended by the sector

Given Area of a sector = 48πcm²

radius of a circle = 16cm

Substituting the given values in the formula to get
`\theta` we have;

`48\pi = (\theta)/(360)*\pi * 16^(2)\\48\pi = (\theta)/(2\pi)*(\pi) * 256\\48 = 256\theta/2\pi\\256\theta = 96\pi\\\theta = 96\pi/256\\\theta = 3\pi/8\ rad`

Answer 2

D.
`(3)/(8) \pi`

Explanation:

The area of a circular sector is defined as

`A=(\pi r^(2) \theta)/(360\°)`

Where
`\theta` is the central angle and
`r` is the radius of the circle.

Replacing given values, we have

`48 \pi = (\pi (16)^(2) \theta)/(360\°)\\ 17,280=256\theta\\\theta = (17,280)/(256) =67(1)/(2)=(135)/(2)`

But, this angle is in degrees, we know that
`\pi = 180\°`

`((135)/(2))\° * (\pi)/(180\°) =0.375 \pi=(3)/(8) \pi`

Therefore, the right answer is D.