Question

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

Answer 1

`Cube : \ V=4500 \ \pi \ in^3\\\\V=(4)/(3)\pi r^3 \\ \\4500 \pi =(4)/(3)\pi r^3 \ \ / \cdot ((3)/(4\pi))\\ \\(3)/(4\pi)\cdot 4500 \pi =(3)/(4\pi)\cdot (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`

Answer 2

`V=(4 \pi r^3)/(3)\\ \\ 4500\pi=(4 \pi r^3)/(3)\\ \\ 13500 \pi=4 \pi r^3\\ \\ r^3=(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}`