Question

Given that the circumference of a circle is 44cm calculate the area​

Answer 1

The area will be 154 cm squared

Explanation:

Circumference of a circle = 2πr

44 = 2 times 22/7 times r

r = 7 cm

Area of circle = πr^2

22/7 times 7^2

22 times 7

154 cm squared

Answer 2

`\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=44 \end{cases}\implies 44=2\pi r\implies \cfrac{44}{2\pi }=r\implies \cfrac{22}{\pi }=r \\\\[-0.35em] ~\dotfill`

`\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=(22)/(\pi ) \end{cases}\implies A=\pi \left( \cfrac{22}{\pi } \right)^2 \\\\\\ A=\pi \cdot \cfrac{22^2}{\pi^2}\implies A=\cfrac{22^2}{\pi }\implies A=\cfrac{484}{\pi }\implies \boxed{A\approx 154.06~cm^2}`