# ACT Math : How to find the volume of a cone

## Example Questions

### Example Question #1 : Solid Geometry

You have an empty cylinder with a base diameter of 6 and a height of 10 and you have a cone full of water with a base radius of 3 and a height of 10.  If you empty the cone of water into the cylinder, how much volume is left empty in the cylinder?

Explanation:

Cylinder Volume =

Cone Volume =

Cylinder Diameter = 6, therefore Cylinder Radius = 3

Empty Volume = Cylinder Volume – Cone Volume

### Example Question #1 : How To Find The Volume Of A Cone

You have two cones, one with a diameter of  and a height of  and another with a diameter of  and a height of . If you fill the smaller cone with sand and dump that sand into the larger cone, how much empty space will be left in the larger cone?

Explanation:

1. Find the volume of each cone:

Cone 1:

Since the diameter is , the radius is .

Cone 2:

Since the diameter is , the radius is .

2. Subtract the smaller volume from the larger volume:

### Example Question #11 : Cones

You have an empty cone and a cylinder filled with water. The cone has a diameter of  and a height of . The cylinder has a diameter of  and a height of . If you dump the water from the cylinder into the cone until it is filled, what volume of water will remain in the cylinder?

Explanation:

1. Find the volumes of the cone and cylinder:

Cone:

Since the diameter is , the radius is .

Cylinder:

Since the diameter is , the radius is .

2. Subtract the cone's volume from the cylinder's volume:

### Example Question #1 : How To Find The Volume Of A Cone

What is the volume of a cone with a height of 7 cm and a radius of 4 cm? Leave your answer in terms of  and as a fraction if need be.

Explanation:

To find the volume of a cone plug the radius and height into the formula for the volume of a cone.

### Example Question #2 : How To Find The Volume Of A Cone

Which of the following will quadruple the volume of a cone?

2. Doubling the height

1 only

3 only

1, 2 and 3

1 and 3

2 only

1 and 3

Explanation:

Bearing in mind the volume formula for a cone:

Because the volume varies by the square of the radius, doubling the radius will quadruple the volume (since .) Because the volume also varies linearly by the height, quadrupling the height will quadruple the volume.

### Example Question #781 : Geometry

What is the volume of a cone with a radius of  and a height of ? Leave your answer in terms of , reduce all fractions.

Explanation:

To find the volume of a cone with radius , and height  use the formula:

.

We plug in our given radius and height to find:

### Example Question #2 : How To Find The Volume Of A Cone

A conical paper cup is being used as a makeshift funnel for motor oil. If the cup is 100 millimeters deep at the center and has a radius of 70 millimeters, how many cubic millimeters of motor oil can it hold at one time? Round your final answer to the nearest integer.

Explanation:

The formula for the volume of a cone is:

With the information we have, we can simply plug values into this equation and solve.

So our cone can hold approximately  cubic millimeters of motor oil.

### Example Question #1 : How To Find The Volume Of A Cone

Find the volume of a cone whose diameter is  and height is .

Explanation:

To find the volume of a cone, simply use the following formula. Thus,

### Example Question #1 : How To Find The Volume Of A Cone

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

Explanation:

To solve simply use the formula for the voluma of a cone. Thus,

### Example Question #1061 : Act Math

What is the volume of a cone with a radius of 3 mm and a height of 6 mm?