Question

A sphere has a volume of Vequals=3600 in cubedin3. Find its surface area.

Answer 1

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4}{3}\pi r^3\qquad \begin{cases} r=radius\\ ------\\ V=3600 \end{cases}\implies 3600=\cfrac{4}{3}\pi r^3 \\\\\\ 3600=\cfrac{4\pi r^3}{3}\implies \sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}=\boxed{r}\\\\ -----------------------------\\\\ \textit{surface area of a sphere}\\\\ S=4\pi r^2\implies S=4\pi \left(\boxed{\sqrt[3]{\cfrac{3\cdot 3600}{4\pi }}} \right)^2$

simplify away