How To Find Volume

How to Find Volume in Standard American English

Volume is a measure of the amount of three-dimensional space occupied by an object. The SI unit of volume is the cubic meter (m³). In the United States, volume is often measured in cubic feet (ft³), cubic inches (in³), or gallons (gal).

There are a number of different formulas that can be used to find the volume of an object, depending on the shape of the object.

Volume of a Rectangular Prism

A rectangular prism is a three-dimensional figure with six rectangular faces. The volume of a rectangular prism is given by the following formula:

V = lwh

where:

• V is the volume of the prism in cubic units
• l is the length of the prism in units
• w is the width of the prism in units
• h is the height of the prism in units

For example, the volume of a rectangular prism that is 5 inches long, 3 inches wide, and 2 inches high is 30 cubic inches.

Volume of a Cube

A cube is a rectangular prism with all six faces being squares. The volume of a cube is given by the following formula:

V = s³

where:

• V is the volume of the cube in cubic units
• s is the length of one side of the cube in units

For example, the volume of a cube that is 5 inches on a side is 125 cubic inches.

Volume of a Cylinder

A cylinder is a three-dimensional figure with two circular faces and a curved surface. The volume of a cylinder is given by the following formula:

V = πr²h

where:

• V is the volume of the cylinder in cubic units
• π is a mathematical constant approximately equal to 3.14159
• r is the radius of the base of the cylinder in units
• h is the height of the cylinder in units

For example, the volume of a cylinder that has a radius of 5 inches and a height of 10 inches is 250π cubic inches.

Volume of a Cone

A cone is a three-dimensional figure with a circular base and a single vertex. The volume of a cone is given by the following formula:

V = (1/3)πr²h

where:

• V is the volume of the cone in cubic units
• π is a mathematical constant approximately equal to 3.14159
• r is the radius of the base of the cone in units
• h is the height of the cone in units

For example, the volume of a cone that has a radius of 5 inches and a height of 10 inches is (1/3)π 5² 10 = 261.8 cubic inches.

Volume of a Sphere

A sphere is a three-dimensional figure that is perfectly round. The volume of a sphere is given by the following formula:

V = (4/3)πr³

where:

• V is the volume of the sphere in cubic units
• π is a mathematical constant approximately equal to 3.14159
• r is the radius of the sphere in units

For example, the volume of a sphere that has a radius of 5 inches is (4/3)π * 5³ = 523.6 cubic inches.

FAQ

What is the difference between volume and capacity?

Volume is a measure of the amount of three-dimensional space occupied by an object, while capacity is a measure of the amount of fluid that an object can hold.

How do I convert cubic feet to gallons?

1 cubic foot is equal to 7.48 gallons.

How do I convert cubic inches to cubic feet?

1 cubic inch is equal to 0.000578 cubic feet.

How do I find the volume of an irregular object?

The volume of an irregular object can be found using a variety of methods, such as the water displacement method or the sand displacement method.