# Pre-Algebra : Volume of a Cone

## Example Questions

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### Example Question #1 : Volume Of A Cone

The standard waffle cone at Cream Canyon Ice Cream Parlor has a diameter of 4 inches.  If the height of the cone is 1.5 times the diameter, what is the volume of the cone?

Explanation:

We must first recall the formula for the volume of a cone.

where  is the radius and  is the height.  The problem is that we are not provided with either the height or the radius.  However, we are told that the height is 1.5 times the diameter.  Since the diameter is 4 inches, we can calculate .  Thus the height of the cone is 6 inches.  We must also recall that the radius of a circle (such as the top of an ice cream cone) is simply half the diameter.  Therefore, if the diameter is 4 inches, the radius is 2 inches.  We now have all of the essential ingredients for volume.

Since our measurements were all in inches, our volume will be in cubic inches.  Therefore, the volume of our ice cream cone is .  Now all we need is a scoop or two of our favorite flavor.

### Example Question #1 : Volume Of A Cone

Which of the following is the volume of the above cone?

cubic centimeters

cubic centimeters

cubic centimeters

cubic centimeters

cubic centimeters

cubic centimeters

Explanation:

The volume of a cone whose height is  and whose base has radius  is defined by the formula

.

Set :

cubic centimeters.

### Example Question #1 : Cones

The volume of a cone whose height is three times the radius of its base is one cubic yard. Give its radius in inches.

Explanation:

The volume of a cone with base radius  and height  is

The height  is three times this, or . Therefore, the formula becomes

Set this volume equal to one and solve for :

This is the radius in yards; since the radius in inches is requested, multiply by 36.

### Example Question #1 : Volume Of A Cone

What is the volume of a cone with a radius of two and a height of three?

Explanation:

Write the formula to find the volume of the cone.

### Example Question #1 : Volume Of A Cone

What is the volume of a cone with a radius of 5 and a height of 6?

Explanation:

Write the formula to find the volume of a cone.

Substitute the dimensions and solve.

### Example Question #15 : Volume

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

Explanation:

The base of a cone has a circular cross section.  Given the base area, there is no need to determine the radius.

Write the formula for the volume of a cone.

The  term represents the base area of the circle.

Substitute all the given values into the volume formula.

### Example Question #1 : Volume Of A Cone

What is the volume of a cone with diameter of 2 and a height of 10?

Explanation:

Write the formula for the volume of a cone.

The radius is half the diameter.

Substitute the radius and the height.

### Example Question #1 : Volume Of A Cone

Find the volume of a cone with a radius of  and a height of .

Explanation:

Write the volume formula for a cone.

Substitute the dimensions.

### Example Question #1 : Volume Of A Cone

Find the volume of the cone that has a radius of  and a height of .

Explanation:

Write the formula to find the volume of a cone.

### Example Question #1 : Volume Of A Cone

Find the volume of a cone with a radius of  and a height of .

Explanation:

Write the formula to find the volume of the vone.

Substitute the dimensions into the formula.

Expand the terms.

Multiply the integers for the volume.

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