Answer:
Option C is correct.
volume of sphere is, [tex]166\frac{2}{3} \pi[/tex] cubic ft
Step-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 ft
Therefore, the volume of sphere is, [tex]166\frac{2}{3} \pi[/tex] cubic ft
