Question

What is the volume of a sphere with a surface area of ​ 100π ​ ft²?

3313π ​ ft³

4823π ​​ ft³

16623π ​ ft³

133313π ft³

Answer 1

Option C is correct.

volume of sphere is,
`166(2)/(3) \pi` cubic ft

Explanation:

Formula for Surface area(S.A) of sphere is given by :

`S.A = 4 \pi r^2`

where r is the radius of the sphere.

As per the given statement:

Surface Area of sphere(S.A) =
`100 \pi` square ft.

Substitute the given values we have;

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

Divide both sides by
`4 \pi` we have;

`25 = r^2`

or

`r = √(25) = 5 ft`

To find the volume of sphere:

Volume of sphere(V) is given by:

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

Substitute the given values we have;

`V = (4)/(3) \pi (5)^3`

or

`V = (4)/(3) \pi 125`

`V = (500)/(3) \pi` ≈ 166.23 cubic ft

Therefore, the volume of sphere is,
`166(2)/(3) \pi` cubic ft