Question

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

Answer 1

Answer:

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

Step-by-step 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

$R^2=144\to R=\sqrt{144}\\\\R=12$

The formula of a volume of a sphere:

$V+\dfrac{4}{3}\pi R^3$

Substitute:

$V=\dfrac{4}{3}\pi(12^3)=\dfrac{4}{3}\pi(1728)=(4)\pi(576)=2304\pi$