Question

The radius of the given circle is 9.2 feet. (a) What is the area of the circle? (b) What is the area of 3 sectors of the circle when it is divided into 8 equal sectors? Express both answers in hundredths.

Answer 1

The area of a circle is given by the formula

`\begin{gathered} A=\pi r^2 \\ \text{where }r\text{ is the radius of the circle} \end{gathered}`

(a) Given that the radius of the circle is 9.2 feet, the area of the circle is.

`\begin{gathered} A=\pi r^2 \\ A=(3.14)(9.2\text{ ft})^2 \\ A=265.7696\text{ ft}^2 \\ \text{when rounded off to hundredths, the area is} \\ A=265.77\text{ ft}^2 \end{gathered}`

(b) Now that we know the area of the circle, we can now solve for the area of 3 sectors of circle when it is divided by 8.

First, divide the area to 8, then multiply it by 3.

`\begin{gathered} A_{3\text{ sectors}}=\frac{265.77\text{ ft}^2}{8}*3 \\ A_{3\text{ sectors}}=33.22125\text{ ft}^2*3 \\ A_{3\text{ sectors}}=99.66375\text{ ft}^2 \\ \text{rounded off to hundredths and we get} \\ A_{3\text{ sectors}}=99.66\text{ ft}^2 \end{gathered}`