Question

Find the volume of a sphere with surface area equal to 100π ft^2

Answer 1

Surface area of sphere =
`4 \pi r^(2)`

Volume of sphere =
`(4)/(3) \pi r^(3)`


`100 \pi =4 \pi r^(2)`

Therefore
`r = 5`


Volume =
`(4)/(3) \pi *5^(3) = (500 \pi )/(3)`

Answer 2

`V=(500)/(3)\ \pi(ft^(3))`

Explanation:

Hello.

to find the volume of a sphere we must know its radius,

we don't know the radius but we have the area

`A=4\pi r^(2) \\ \\isolating\ r\\\\A=4\pi r^(2)\\r=\sqrt{(A)/(4\pi ) } \\r=\sqrt{(100\ ft^(2) )/(4\pi)} \\\\ r= \sqrt{25\ ft^(2) }\\ r=5\ ft\\`

Now, replacing this value in the volume equation

`V=(4\pi r^(3) )/(3) \\V=(4\pi\ (5\ ft)^(3) )/(3)\\ V=(4\pi\ (125 ft^(3)) )/(3)\\V=(500)/(3)\ \pi (ft^(3))\\\\\\`

have a great day