Question

The circumference of the hub cap of a tire is 83. 59 centimeters. Find the area of this hub cap. Use 3. 14 for π. Use pencil and paper. If the circumference of the hub cap were​ smaller, explain how this would change the area of the hub cap.


​(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as​ needed. )

Answer 1

$\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=83.59 \end{cases}\implies 83.59=2\pi r\implies \cfrac{83.59}{2\pi }=r\implies \cfrac{41.795}{\pi }=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \implies \qquad A=\pi \left( \cfrac{41.795}{\pi } \right)^2\implies \stackrel{using~\pi =3.14}{A\approx 556}$