Answer:
[tex]\large\boxed{C)\ 166\dfrac{2}{3}\pi\ ft^3}[/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.=100\pi\ ft^2[/tex]
Substitute:
[tex]4\pi R^2=100\pi[/tex] divide both sides by 4π
[tex]R^2=25\to R=\sqrt{25}\\\\R=5\ ft[/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(5)^3=\dfrac{4}{3}\pi(125)=\dfrac{500}{3}\pi=166\dfrac{2}{3}\pi[/tex]
