What is the volume of a sphere with a surface area of ​ 100π ​ ft²?3313π ​ ft³4823π ​​ ft³16623π ​ ft³133313π ft³

Answer: Option C is correct.volume of sphere is, [tex]166\frac{2}{3} \pi[/tex] cubic ftStep-by-step explanation:Formula for Surface area(S.A) of sphere is given by :[tex]S.A = 4 \pi r^2[/tex]where r is the radius of the sphere.As per the given statement:Surface Area of sphere(S.A) = [tex]100 \pi[/tex] square ft.Substitute the given values we have;[tex]100 \pi = 4\pi r^2[/tex]Divide both sides by [tex]4 \pi[/tex] we have;[tex]25 = r^2[/tex]or[tex]r = \sqrt{25} = 5 ft[/tex]    To find the volume of sphere:Volume of sphere(V) is given by:[tex]V = \frac{4}{3} \pi r^3[/tex]Substitute the given values we have;[tex]V = \frac{4}{3} \pi (5)^3[/tex]or[tex]V = \frac{4}{3} \pi 125[/tex][tex]V = \frac{500}{3} \pi[/tex] ≈ 166.23 cubic ftTherefore, the volume of sphere is, [tex]166\frac{2}{3} \pi[/tex] cubic ft