Question

The circumference of a circle is 11pi inches. What is the area, in square inches, of the circle? Express your answer in terms of pi. and....SHOW YOUR WORK.

Answer 1

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=11\pi \end{cases}\implies 11\pi =2\pi r\implies \cfrac{11\pi }{2\pi }=r\implies \boxed{\cfrac{11}{2}=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies A=\pi \left( \cfrac{11}{2}\right)^2\implies A=\pi \left( \cfrac{11^2}{2^2}\right)\implies A=\cfrac{121\pi }{4}$