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

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3 months 2022-02-15T14:17:35+00:00 1 Answer 0 views 0

1130.97336 units^3

Step-by-step explanation:

The volume of a cylinder can be found using:

$$v=\pi r^2h$$

We have the area of the base, but not the radius

$$a=\pi r^2$$

We know the area is $$36\pi$$, so we can substitute that in for a

$$36\pi =\pi r^2$$

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

$$v=\pi r^2h$$

$$v=\pi 6^210$$

Solve the exponent

$$v=\pi 36(10)$$

$$v=\pi 360$$

v=1130.97336

The volume is 1130.97336 units^3