Question

A sector with an area of 26pie cm^2 has a radius of 6 cm. What is the central angle measure of the sector in radians?

Answer 1

Answer:

The central angle measure of the sector in radians is $\theta=\frac{13}{9}$.

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc. It resembles a "pizza" slice.

The area of a sector when the central angle is in radians is given by

                                                    $A=(\frac{\theta}{2})\cdot r^2$

where

r = radius

θ = central angle in radians

We know that the area of the sector is $26 \:cm^2$ and the radius is 6 cm. Applying the above formula and solving for the central angle ($\theta$) we get that

                                                   $26=(\frac{\theta}{2})\cdot (6)^2\\\\\left(\frac{\theta}{2}\right)\left(6\right)^2=26\\\\\frac{\frac{\theta}{2}\cdot \:6^2}{36}=\frac{26}{36}\\\\\frac{\theta}{2}=\frac{13}{18}\\\\\theta=\frac{13}{9}$