Question

What is the circumference of a circle with an area of 113.04 cm²?

Answer 1

$\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=113.04 \end{cases}\implies 113.04=\pi r^2\implies \cfrac{113.04}{\pi }=r^2 \\\\\\ \sqrt{\cfrac{113.04}{\pi }}=r \\\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\qquad \qquad \implies C=2\pi \left( \sqrt{\cfrac{113.04}{\pi }} \right)\implies \stackrel{using~\pi = 3.14}{C\approx 37.68}$

Answer 2

Answer

= 37.68 cm

Explanation

The area of a circle is given by:

Area = πr²= 113.04

r² = 113.04 /π

= 113.04 / 3.14

= 36

r =√36

=6 cm

Circumference = 2πr

= 2×π×6

= 37.68 cm