Question

A sphere has a volume of 4,500 cubic feet. Find the radius of the sphere.

Answer 1

Explanation:

Volume of a sphere is

`v = (4)/(3) * \pi * {r}^(3)`

We are given the volume, v, and asked to find the radius, r.

Substitute 4500 ft^3 for v, solve for r.

`4500 = (4)/(3) * \pi * {r}^(3)`

Multiply both sides by 3/4 to eliminate 4/3

`(3)/(4) * 4500 = (4)/(3) * \pi * {r}^(3) * (3)/(4)`

`(13500)/(4) = \pi * {r}^(3) \: \\ then \: divide \: by \: \pi`

`(3375)/(\pi) = {r}^(3 \: \: take \: the \: cubed \: root \: of \: both \: sides)`

`\frac{ \sqrt[3]{ {15}^(3) } }{ \sqrt[3]{\pi} } = \sqrt[3]{r}`

`\frac{15}{ \sqrt[3]{\pi} } = r`

That approximates to 10.27 ft^3