# Pre-Algebra : Volume of a Cylinder

## Example Questions

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### Example Question #51 : Volume

Find the volume of a cylinder with a base area of  and a height of .

Explanation:

Write the formula to find the volume of the cylinder.

Because the base of the cylinder is a circle, the term  represents the area of the circular base, which is already given.

Multiply the area with the height to obtain the volume.

### Example Question #12 : Volume Of A Cylinder

Solve for the volume of a cylinder if the radius is  and the height is twice the radius.

Explanation:

Write the formula for the volume of the cylinder.

The height is 14, since it is twice the radius.  Substitute the dimensions.

### Example Question #13 : Volume Of A Cylinder

Solve for the volume of a cylindrical soda can if the base perimeter is  and the height is .

Explanation:

Write the formula for the volume of a cylinder.

The radius is unknown.  In order to solve for the radius, use the base perimeter as a given to solve for the radius.  The base perimeter is the circular circumference.

Write the formula for the circle's circumference.

Substitute the base perimeter.

Divide  on both sides to solve for the radius.

Substitute the radius and the height into the volume formula.

### Example Question #14 : Volume Of A Cylinder

You have a can of soup that looks like the following.

The height is 5 in and the diameter is 4 in.  If , find the volume of the soup can.  Round to the nearest tenths.

Explanation:

The formula to find the volume of a cylinder is

We know the diameter of the cylinder is 4in.  The radius is half the diameter, so the radius of the cylinder is 2in.  We know,

When we substitute into the formula, we get

Therefore, the volume of the soup can is

### Example Question #15 : Volume Of A Cylinder

A cylinder has a volume of . If the height of the cylinder is , what is the radius?

Explanation:

The formula for the volume of a cylinder is:

To find the radius, we simply plug in the given values and solve for :

Therefore, the radius of the circle is .

### Example Question #52 : Volume

If Cindy has a cylindrical bucket filled with sand, how much sand does it contain if area of the circular bottom is  inches and the heigh of the bucket is  inches?

Explanation:

To find the volume of a cylinder, the formula is .
Normally, you would simply input the radius given for "" and the height given for "". However, the question did not directly give us the radius; it gave us the area of the circular bottom.

Now examine the volume formula closely, and you will see that the formula for the area of a circle is hidden inside the volume formula. If  is the area of a circle, then we can simply multiply the area of the circle given by the height given.

V = area of the circle x height

cubed inches

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