Question

4. Find the radius of a circle that has a sector area of 76 square inches cut off by a centralangle of 210°.

Answer 1

The sector area of a circle is given by the formula:

`A=\pi r^2(\theta)/(360)`

We know that the sector area is 76 square inches and the central angle is 210, then by replacing those values we have:

`76in^2=\pi r^2(210)/(360)`

Now, solve for r:

`\begin{gathered} 76in^2\cdot(360)/(210)=\pi r^2(210)/(360)\cdot(360)/(210) \\ \text{Simplify} \\ 76in^2\cdot(360)/(210)=\pi r^2 \\ 76in^2\cdot1.71=\pi r^2 \\ 130.29in^2=\pi r^2 \\ r^2=(130.29in^2)/(\pi) \\ r^2=41.47in^2 \\ r=\sqrt[]{41.47in^2} \\ r=6.44in \end{gathered}`

Thus, the radius of the circle is 6.44 inches.