Given in the question:
a.) The circumference of a circle is 24pi ft.
Recall: Formula in getting the circumference of a circle.
[tex]\text{ Circumference = 2}\pi r[/tex]Let's first determine the radius of the circle.
[tex]\text{ Circumference = 2}\pi r[/tex][tex]\text{ 24}\pi\text{ = 2}\pi r[/tex][tex]\text{ }\frac{\text{24}\pi}{2\pi}\text{ = }\frac{\text{2}\pi r}{2\pi}[/tex][tex]\text{ 12 = r}[/tex]Therefore, the radius of the circle is 12 Ft.
Recall: Formula in getting the area of the circle.
[tex]\text{ Area = }\pi r^2[/tex]We get,
[tex]\text{ Area = }\pi r^2[/tex][tex]\text{ = }\pi(12)^2[/tex][tex]\text{ Area = 144}\pi\text{ squared ft.}[/tex]The area of the circle is, therefore, 144pi sq. ft.
