Question

A sphere has a volume of 500/3 π cubic centimeters. What is the total surface area , in square centimeters, of the sphere

Answer 1

Answer:

$\large\boxed{S.A.=100\pi\ cm^3\approx314\pi\ cm^2}$

Step-by-step explanation:

The formula of a volume of a sphere:

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

R - radius

We have

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

Substitute and solve for R:

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

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

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

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

The formula of a Surface Area os a sphere:

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

Substitute:

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

$\pi\apprx3.14\to S.A.\approx(100)(3.14)=314\ cm^2$