Question

A sphere has a volume of V=900 in^3 . Find the surface area

Answer 1

1) Considering the formula for the Volume of the Sphere:

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

We can plug into that formula the Volume, and solve for r. This way we get the radius of this sphere.

`\begin{gathered} 900=(4)/(3)\pi r^3 \\ \\ 3*900=3*(4)/(3)\pi r^3 \\ \\ 2700=4\pi r^3 \\ \\ 4\pi r^3=2700 \\ \\ (4\pi r^3)/(4\pi)=(2700)/(4\pi) \\ \\ r^3=(2700)/(4\pi) \\ \\ r=\sqrt[3]{(2700)/(4\pi)} \\ \\ r\approx5.989 \end{gathered}`

2) On the other hand, we also need the formula to find the Surface Area:

`\begin{gathered} A=4\pi r^2 \\ \\ A=4\pi(5.989)^2 \\ \\ A\approx450\:in² \end{gathered}`

Rounded to the nearest whole number as requested. So, that is the answer.