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

`\large\boxed{C)\ 166(2)/(3)\pi\ ft^3}`

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=√(25)\\\\R=5\ ft`

The formula of a volume of a sphere:

`V=(4)/(3)\pi R^3`

Substitute:

`V=(4)/(3)\pi(5)^3=(4)/(3)\pi(125)=(500)/(3)\pi=166(2)/(3)\pi`