Answer:
[tex]\large\boxed{V=2304\pi}[/tex]
Step-by-step explanation:
The formula of a surface area of a sphere:
[tex]S.A.=4\pi R^2[/tex]
R - radius
We have
[tex]S.A.=576\pi[/tex]
Substitute and solve for R:
[tex]4\pi R^2=576\pi[/tex] divide both sides by π
[tex]4R^2=576[/tex] divide both sides by 4
[tex]R^2=144\to R=\sqrt{144}\\\\R=12[/tex]
The formula of a volume of a sphere:
[tex]V+\dfrac{4}{3}\pi R^3[/tex]
Substitute:
[tex]V=\dfrac{4}{3}\pi(12^3)=\dfrac{4}{3}\pi(1728)=(4)\pi(576)=2304\pi[/tex]
