Answer:
1130.97336 units^3
Step-by-step explanation:
The volume of a cylinder can be found using:
[tex]v=\pi r^2h[/tex]
We have the area of the base, but not the radius
[tex]a=\pi r^2[/tex]
We know the area is [tex]36\pi[/tex], so we can substitute that in for a
[tex]36\pi =\pi r^2[/tex]
We want to find r, so we need to isolate it
Divide both sides by pi
36=r^2
Take the square root of both sides
6=r
Now we know the radius, and can substitute it into the volume formula, and we can substitute the height (10) in
[tex]v=\pi r^2h[/tex]
[tex]v=\pi 6^210[/tex]
Solve the exponent
[tex]v=\pi 36(10)[/tex]
[tex]v=\pi 360[/tex]
v=1130.97336
The volume is 1130.97336 units^3
