1 Answer

Aaronp · Answer 1 · 2020-02-19T23:14:36+0000

Answer:

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

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:

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

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