Answer:
[tex]\large\boxed{S.A.=100\pi\ cm^3\approx314\pi\ cm^2}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have
[tex]V=\dfrac{500}{3}\pi\ cm^3[/tex]
Substitute and solve for R:
[tex]\dfrac{500}{3}\pi=\dfrac{4}{3}\pi R^3[/tex] divide both sides by π
[tex]\dfrac{500}{3}=\dfrac{4}{3}R^3[/tex] multiply both sides by 3
[tex]500=4R^3[/tex] divide both sides by 4
[tex]125=R^3\to R=\sqrt[3]{125}\\\\R=5\ cm[/tex]
The formula of a Surface Area os a sphere:
[tex]S.A.=4\pi R^2[/tex]
Substitute:
[tex]S.A.=4\pi(5^2)=4\pi(25)=100\pi\ cm^2[/tex]
[tex]\pi\apprx3.14\to S.A.\approx(100)(3.14)=314\ cm^2[/tex]
