Question

The area of a compact disc is 452 4/7 square centimeters. What is the diameter of a compact disc ? Use 22/7 as an approximation for pie?

Answer 1

`\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=452(4)/(7) \end{cases}\implies 452(4)/(7)=\pi r^2\implies \cfrac{3168}{7}=\pi r^2 \implies \cfrac{3168}{7\pi }=r^2 \\\\\\ \stackrel{\pi =(22)/(7)}{\cfrac{3168}{7\cdot (22)/(7)}}=r^2\implies \cfrac{3168}{22}=r^2\implies 144=r^2\implies √(144)=r\implies 12=r \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{diameter=2r}{d=24}~\hfill`