Question

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

Answer 1

Answer:

D. $\frac{3}{8} \pi$

Step-by-step explanation:

The area of a circular sector is defined as

$A=\frac{\pi r^{2} \theta}{360\°}$

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

Replacing given values, we have

$48 \pi = \frac{\pi (16)^{2} \theta}{360\°}\\ 17,280=256\theta\\\theta = \frac{17,280}{256} =67\frac{1}{2}=\frac{135}{2}$

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

$(\frac{135}{2})\° \times \frac{\pi}{180\°} =0.375 \pi=\frac{3}{8} \pi$

Therefore, the right answer is D.

Answer 2

Answer:

The central angle is 3π/8 rad

Step-by-step explanation:

Area of a sector is expressed as $\frac{\theta}{360^{0} } *\pi r^{2}$

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;

$48\pi = \frac{\theta}{360}*\pi * 16^{2}\\48\pi = \frac{\theta}{2\pi}*(\pi) * 256\\48 = 256\theta/2\pi\\256\theta = 96\pi\\\theta = 96\pi/256\\\theta = 3\pi/8\ rad$