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

Answer:

The volume of the sphere is:

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

Step-by-step 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:

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

Here we have:

Surface area of sphere=  36 pi ft square.

i.e.

$4\pi r^2=36\pi\\\\i.e.\\\\r^2=\dfrac{36\pi}{4\pi}\\\\i.e.\\\\r^2=\dfrac{36}{4}\\\\i.e.\\\\r=\sqrt{\dfrac{36}{4}}\\\\i.e.\\\\r=\sqrt{9}\\\\i.e.\\\\r=3\ units$

and the Volume of sphere will be:

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