The height of a cylinder is 10 and the area of a base is 36 pi square units. What is the volume in cubic units Question The height of a cylinder is 10 and the area of a base is 36 pi square units. What is the volume in cubic units in progress 0 Math Everleigh 3 months 2022-02-15T14:17:35+00:00 2022-02-15T14:17:35+00:00 1 Answer 0 views 0

## Answers ( )

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