Given:
The area of the given sphere = 36π in²
To find the volume of the given sphere.
We need to find the radius first.
Formula
- The area of a sphere [tex]A = 4\pi r^{2}[/tex]
- The volume of the sphere [tex]V = \frac{4}{3} \pi r^{3}[/tex]
where, r be the radius of the sphere.
Now,
According to the problem,
[tex]4\pi r^{2} = 36\pi[/tex]
or,[tex]4r^{2} = 36\\[/tex] [ Eliminating π from both the side]
or, [tex]r^{2} = \frac{36}{4}[/tex]
or, [tex]r = \sqrt{9}[/tex]
or, [tex]r = 3[/tex]
So,
The radius of the sphere is 3 inches
Therefore,
The volume of the sphere is
[tex]V = \frac{4}{3} \pi (3)^{3}[/tex]
or, [tex]V = 36\pi[/tex]
Hence,
The volume of the sphere is 36π cube inches.
