Question

Find the radius of the circle below. Round your answer to the nearest tenth. You mustshow work for full credit.A= 31.2 cm 2.256A

Answer 1

The given information is:

- The area of the sector of the circle is 31.2 cm^2.

- The exterior of the sector angle is 256°.

The area of the sector is given by the formula:

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

Where theta is the sector angle and r is the radius of the circle.

The whole circle measures 360°, so the sector angle can be found as follows:

`\begin{gathered} \theta+256\degree=360\degree \\ \theta=360\degree-256\degree \\ \theta=104\degree \end{gathered}`

Now, replace theta and the area value in the formula to solve for r:

`\begin{gathered} 31.2=(104)/(360)*\pi r^2 \\ \\ 31.2*(360)/(104)=\pi r^2 \\ \\ 108=\pi r^2 \\ \\ r^2=(108)/(\pi) \\ \\ r^2=34.4 \\ \\ r=√(34.4) \\ \\ r=5.9 \end{gathered}`

The radius of the circle is 5.9 cm.