Question

The surface area of a sphere is 576pi square units. Which choice represents the volume of the sphere?

Answer 1

`\large\boxed{V=2304\pi}`

Explanation:

The formula of a surface area of a sphere:

`S.A.=4\pi R^2`

R - radius

We have

`S.A.=576\pi`

Substitute and solve for R:

`4\pi R^2=576\pi` divide both sides by π

`4R^2=576` divide both sides by 4

`R^2=144\to R=√(144)\\\\R=12`

The formula of a volume of a sphere:

`V+(4)/(3)\pi R^3`

Substitute:

`V=(4)/(3)\pi(12^3)=(4)/(3)\pi(1728)=(4)\pi(576)=2304\pi`