Question

A sphere has a volume of 4500pi cubic inches. find the surface area of the sphere.

Answer 1

$V=\frac{4 \pi r^3}{3}\\ \\ 4500\pi=\frac{4 \pi r^3}{3}\\ \\ 13500 \pi=4 \pi r^3\\ \\ r^3=\frac{13500 \pi}{4 \pi}\\ \\ r^3=3375 \\ \\ \boxed{r=15 in}$

$S=4 \pi r^2\\ \\ S=4 \pi 15^2\\ \\ \boxed{S=900 \pi \ in^2}$

Answer 2

$Cube : \ V=4500 \ \pi \ in^3\\\\V=\frac{4}{3}\pi r^3 \\ \\4500 \pi =\frac{4}{3}\pi r^3 \ \ / \cdot (\frac{3}{4\pi})\\ \\\frac{3}{4\pi}\cdot 4500 \pi =\frac{3}{4\pi}\cdot \frac{4}{3} \pi r^3\\ \\r^3 =3*1125$

$r^3 = 3375 \\\\r=\sqrt[3]{3375}\\ \\r=15 \ in \\ \\ the \ surface \ area : \\\\SA = 4 \pi r^2 \\ \\SA=4 \pi \cdot 15^2 = 4\cdot 225 \pi = 900 \pi \ in^2$