Question

A circle has a radius of 5 inches (What is the measure, in radians, of this central angle?

Answer 1

Answer:

Step-by-step explanation:

Given

Circle has radius $r=5 in.$

Area of the sector is given by

$A_s=\frac{\theta }{2\pi }\times \pi r^2$

if $A_s$ is one-sixth  of area of circle then

$A_s=\frac{\pi r^2}{6}$

$\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2$

$\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian$

If $A_s$ is one-fourth of area of circle then

$A_s=\frac{\pi r^2}{4}$

$\theta =\frac{2\pi }{4}$

$\theta =\frac{\pi }{2}$