Question

A sphere has a surface area of 36 pi ft square. find the volume of the sphere

Answer 1

SA=4pir^2
V=(4/3)hpir^2


given
SA=36pi
36pi=4pir^2
divide by 4pi
9=r^2
sqrt both sides
3=r


v=(4/3)pir^3
v=(4/3)pi3^3
V=4pi9
v=36pi

36pi cubic feet

Answer 2

The volume of the sphere is:

`36\pi\ \text{cubic\ feet}`

Explanation:

Let us consider a sphere with radius r.

We know that the surface area(SA) of the sphere is given by:

`SA=4\pi r^2`

and the volume(V) of the sphere is given by:

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

Here we have:

Surface area of sphere= 36 pi ft square.

i.e.

`4\pi r^2=36\pi\\\\i.e.\\\\r^2=(36\pi)/(4\pi)\\\\i.e.\\\\r^2=(36)/(4)\\\\i.e.\\\\r=\sqrt{(36)/(4)}\\\\i.e.\\\\r=√(9)\\\\i.e.\\\\r=3\ units`

and the Volume of sphere will be:

`V=(4)/(3)\pi r^3\\\\i.e.\\\\V=(4)/(3)\pi (3)^3\\\\i.e.\\\\V=36\pi\ \text{cubic\ feet}`