Given
[tex]circumference\text{ of circle = 24}\pi\text{ in}[/tex]Recall that the formula for the circumference of a circle C is:
[tex]C\text{ = 2}\pi r[/tex]Using the formula, we can find the radius of the circle as shown:
[tex]\begin{gathered} 2\pi r\text{ = 24}\pi \\ Divide\text{ both sides by 2}\pi \\ r\text{ = }\frac{24\pi}{2\pi} \\ r\text{ = 12 in} \end{gathered}[/tex]The area A of a circle can be found using the formula:
[tex]A\text{ = }\pi r^2[/tex]Substituting the value obtained:
[tex]\begin{gathered} A\text{ = }\pi\text{ }\times\text{ 12}^2 \\ =\text{ 144}\pi\text{ in}^2 \end{gathered}[/tex]The area is 144π square in
