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

The central angle measure of the sector in radians is
`\theta=(13)/(9)`.

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=((\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=((\theta)/(2))\cdot (6)^2\\\\\left((\theta)/(2)\right)\left(6\right)^2=26\\\\((\theta)/(2)\cdot \:6^2)/(36)=(26)/(36)\\\\(\theta)/(2)=(13)/(18)\\\\\theta=(13)/(9)`