Answer:
[tex]\large\boxed{18,432\pi\ yd^3}[/tex]
Step-by-step explanation:
The formula of a surface area of a sphere:
[tex]S.A.=4\pi R^2[/tex]
We have Surface Area:
[tex]S.A.=2,304\pi\ yd^2[/tex]
Substitute:
[tex]4\pi R^2=2,304\pi\qquad\text{divide both sides by}\ 4\pi\\\\R^2=\dfrac{2,304\pi}{4\pi}\\\\R^2=576\to R=\sqrt{576}\\\\R=24\ yd[/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(24)^3=\dfrac{4}{3}\pi(13,824)=4\pi(4,608)=18,432\pi\ yd^3[/tex]
