Question

How do I solve this?

Answer 1

Answer:

C. 100π

Step-by-step explanation:

The formula of a volume of a sphere:

$V=\dfrac{4}{3}\pi R^3$

The formula of a surface area of a sphere:

$S.A.=4\pi R^2$

R - radius

We need the length of the radius to calculate the area of the sphere.

Calculate it from the volume of the sphere.

We have a volume:

$V=\dfrac{500}{3}\pi\ cm^3$

Substitute to the formula of a volume:

$\dfrac{4}{3}\pi R^3=\dfrac{500}{3}\pi R^3$     divide both sides by π

$\dfrac{4}{3}R^3=\dfrac{500}{3}$            multiply both sides by 3

$4R^3=500$           divide both sides by 4

$R^3=125\to R=\sqrt[6]{125}\\\\R=5\ cm$

Put the value of radius to the formula of a surface area of a sphere:

$S.A.=4\pi(5^2)=4\pi(25)=100\pi\ cm^2$