Question

PLEASE HELP ASAP !!

What is the volume of a sphere with a surface area of 100pi ft^2?

A) 33 1/3pi ft^3
B)48 2/3pi fr^3
C)166 2/3pi ft^3
D)1333 1/3pi ft^3

Answer 1

Answer:

$\large\boxed{C)\ 166\dfrac{2}{3}\pi\ ft^3}$

Step-by-step explanation:

The formula of a surface area of a sphere:

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

R - radius

We have:

$S.A.=100\pi\ ft^2$

Substitute:

$4\pi R^2=100\pi$                 divide both sides by 4π

$R^2=25\to R=\sqrt{25}\\\\R=5\ ft$

The formula of a volume of a sphere:

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

Substitute:

$V=\dfrac{4}{3}\pi(5)^3=\dfrac{4}{3}\pi(125)=\dfrac{500}{3}\pi=166\dfrac{2}{3}\pi$