Question

Question is in image and showing work isn’t necessary unless wanted to

Answer 1

Given,

The diameter of the circle is 18 feet.

The measure of the arc is 30 degree.

Required:

The area of the sector.

The radius of the circle is calculated as:

`\begin{gathered} Radius\text{ =}(diameter)/(2) \\ Radius\text{ =}(18)/(2) \\ Rad\imaginaryI us=9\text{ feet} \end{gathered}`

The area of the sector of the circle is calculated as:

`Area\text{ =}(\theta)/(360^(\circ))*2\pi(radius)`

Substituting the values then,

`\begin{gathered} Area\text{ =}(30^(\circ))/(360^(\circ))*2*(22)/(7)*9 \\ =(3)/(36)*(44)/(7)*9 \\ =(1)/(4)*(44)/(7)*3 \\ =(11)/(7)*3 \\ =(33)/(7)\text{ feet}^2 \end{gathered}`

Hence, the area of the sector is 33/7 square feet.