Question

What is the volume of a sphere with surface area of 25 pi yd squared?

Answer 1

`\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=25\pi \end{cases}\implies 25\pi =4\pi r^2 \\\\\\ \cfrac{25\pi }{4\pi }=r^2\implies \cfrac{25}{4}=r^2\implies \sqrt{\cfrac{25}{4}}=r\implies \cfrac{√(25)}{√(4)}=r\implies \cfrac{5}{2}=r \\\\[-0.35em] ~\dotfill`

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( (5)/(2) \right)^3}{3}\implies V=\cfrac{4\pi \cdot (125)/(8)}{3}\implies V=\cfrac{(500\pi )/(8)}{~~(3)/(1)~~} \\\\\\ V=\cfrac{500\pi }{8}\cdot \cfrac{1}{3}\implies V=\cfrac{500\pi }{24}\implies V=\cfrac{125\pi }{6}\implies V\approx 65.45`