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:
[tex]\begin{gathered} Radius\text{ =}\frac{diameter}{2} \\ Radius\text{ =}\frac{18}{2} \\ Rad\imaginaryI us=9\text{ feet} \end{gathered}[/tex]The area of the sector of the circle is calculated as:
[tex]Area\text{ =}\frac{\theta}{360^{\circ}}\times2\pi(radius)[/tex]Substituting the values then,
[tex]\begin{gathered} Area\text{ =}\frac{30^{\circ}}{360^{\circ}}\times2\times\frac{22}{7}\times9 \\ =\frac{3}{36}\times\frac{44}{7}\times9 \\ =\frac{1}{4}\times\frac{44}{7}\times3 \\ =\frac{11}{7}\times3 \\ =\frac{33}{7}\text{ feet}^2 \end{gathered}[/tex]Hence, the area of the sector is 33/7 square feet.