# GED Math : Volume of a Cylinder

## Example Questions

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

One cubic foot is equal to (about) 7.5 gallons.

A circular swimming pool has diameter 60 feet and depth five feet throughout. Using the above conversion factor, how many gallons of water does it hold?

Use 3.14 for .

Explanation:

The pool can be seen as a cylinder with depth (or height) 5 feet, and a base with diameter 60 feet - and radius half this, or 30 feet. The capacity of the pool is the volume of this cylinder, which is

cubic feet.

One cubic foot is equal to 7.5 gallons, so multiply:

gallons

### Example Question #2 : Volume Of A Cylinder

A cylindrical bucket is one foot high and one foot in diameter. It is filled with water, which is then emptied into an empty barrel three feet high and two feet in diameter. What percent of the barrel has been filled?

Explanation:

The volume of a cylinder is

The bucket has height  and diameter 1, and,subsequently, radius ; its volume is

cubic feet

The barrel has height  and diameter 2,and, subsequently, radius ; its volume is

The volume of the bucket is

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

A water tank takes the shape of a closed cylinder whose exterior has height 30 feet and a base with radius 10 feet; the tank is three inches thick throughout. To the nearest hundred, how many cubic feet of water does the tank hold?

You may use 3.14 for .

Explanation:

Three inches is equal to 0.25 feet, so the height of the interior of the tank is

inches.

The radius of the interior of the tank is

inches.

The amount of water the tank holds is the volume of the interior of the tank, which is

cubic feet.

This rounds to 8,800 cubic feet.

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

The above diagram is one of a cylindrical tub. The company wants to make a cylindrical tub with three times the volume, but whose base is only twice the radius. How high should this new tub be?

Explanation:

The volume of the given tub can be expressed using the following formula, setting  and :

cubic inches.

The new tub should have three times this volume, or

cubic inches.

The radius is to be twice that of the above tub, which will be

inches.

The height can therefore be calculated as follows:

inches

### Example Question #5 : Volume Of A Cylinder

Refer to the cylinder in the above diagram.

A cone has twice the volume and twice the height of the cylinder. What is the radius of the base of the cone (nearest tenth of an inch, if applicable)?

Explanation:

The formula for the volume of the cylinder is

where  and  are the base radius and height of the cylinder.

Set  in the formula to find the volume of the cylinder:

The cylinder will have volume twice this, or , and height twice the height of the cylinder, which is 80 inches.

The formula for the volume of the cone is

,

so we set  and  and solve for :

inches.

### Example Question #6 : Volume Of A Cylinder

The above diagram is one of a cylindrical tub. The tub is holding water at 40% capacity. To the nearest cubic foot, how much more water can it hold?

Explanation:

The volume of the cylinder can be calculated using the following formula, setting  and :

cubic inches.

The tub is 40% full, so it is 60% empty; it can hold

more cubic inches of water.

The problem asks for the number of cubic feet, so divide by the cube of 12, or 1,728:

The correct response is 27 cubic feet.

### Example Question #7 : Volume Of A Cylinder

A circular swimming pool has diameter 40 feet and depth six feet throughout. How many cubic feet of water does it hold? (nearest cubic foot)

Use 3.14 as the value of .

Explanation:

The pool can be seen as a cylinder with depth (or height) six feet and a base with diameter 40 feet - and radius half this, or 20 feet. The capacity of the pool is the volume of this cylinder, which is

cubic feet.

### Example Question #8 : Volume Of A Cylinder

A circular swimming pool has diameter 20 meters and depth 2.5 meters throughout. How many cubic meters of water does it hold?

Use 3.14 for .

Explanation:

The pool can be seen as a cylinder with depth (or height) 2.5 m, a base with diameter 20 m, and a radius of half this, or 10 m. The capacity of the pool is the volume of this cylinder, which is

cubic meters.

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

Find the volume of a cylinder with a radius of 2, and a height of 11.

Explanation:

Write the volume for the cylinder.

Substitute the dimensions.

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

Find the volume of a cylinder with a radius of 2, and a height of 15.