Question

Find the surface area (in terms of pi) of a sphere of its volume is 36pi.

Answer 1

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=36\pi \end{cases}\implies 36\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{36\pi}{4\pi } \cdot 3=r^3 \\\\\\ 9\cdot 3=r^3\implies 27=r^3\implies \sqrt[3]{27}=r\implies \boxed{3=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad SA=4\pi (3)^2\implies SA=36\pi`

Answer 2

113.04 cubic units

Explanation:

(4×3.14×3×3×3)/3=113.04 cubic units.