What is volume?
Volume is how much space a 3-D shape takes up, measured in cubic units: a cube 1 foot on each side is 1 cubic foot (ft³). For a container, it is how much it holds. A US gallon is 231 cubic inches, so 1 cubic foot holds 7.4805 gallons, and a cubic meter holds 1,000 liters.
Source OpenStax · Prealgebra 2e, 9.6 Solve Geometry Applications: Volume and Surface Area ↗Common Core State Standards · Grade 5, volume = length × width × height (5.MD.C.5b) ↗NIST Handbook 44 (2026) · Appendix C, General Tables of Units of Measurement (gallon = 231 cubic inches) ↗
How to calculate volume
Here it is with your numbers:
- V = 4 × 3 × 2
- V = 24 ft³
- US gallons: 24 ft³ × 1,728 ÷ 231 = 179.5325
It means the box holds 24 cubic feet, or 179.5325 US gallons of water.
We use π to full precision. Textbooks often round it to 3.14, which makes their answers a little smaller: a sphere with a 6-inch radius is 904.78 in³ here and 904.32 in³ with 3.14.
Volume formulas
| Shape | Volume |
|---|---|
| Box (rectangular prism) | length × width × height |
| Cube | side³ |
| Cylinder | π × radius² × height |
| Sphere | 4/3 × π × radius³ |
| Cone | 1/3 × π × radius² × height |
| Pyramid | 1/3 × length × width × height |
A cone holds a third of a cylinder with the same radius and height, and a pyramid a third of the box around it.
Source OpenStax · Calculus Volume 1, 6.2 Determining Volumes by Slicing (pyramid) ↗Common Core State Standards · Grade 8, volumes of cones, cylinders and spheres (8.G.C.9) ↗
FAQs
What is a formula for volume?
It depends on the shape. A box is length × width × height, a cube is side³, a cylinder is π × radius² × height, a sphere is 4/3 × π × radius³, and a cone is 1/3 × π × radius² × height.
Source OpenStax · Prealgebra 2e, 9.6 Solve Geometry Applications: Volume and Surface Area ↗
How do you calculate volume in gallons?
Work out the volume in cubic inches and divide by 231, because a US gallon is 231 cubic inches. From cubic feet, multiply by 1,728 ÷ 231, which is 7.4805 gallons per cubic foot.
What is the volume of a 3x3x3 cube?
27 cubic units: 3 × 3 × 3. If the sides are 3 feet, that is 27 cubic feet, the same as 1 cubic yard.
Source OpenStax · Prealgebra 2e, 9.6 Solve Geometry Applications: Volume and Surface Area ↗
How to find the volume of a cylinder?
Multiply π × radius² × height. The radius is half the distance across. A cylinder 3 inches in radius and 5 inches high holds π × 9 × 5, which is 45π, or 141.37 cubic inches.
Sources
- OpenStax: Prealgebra 2e, 9.6 Solve Geometry Applications: Volume and Surface Area
- OpenStax: Calculus Volume 1, 6.2 Determining Volumes by Slicing (pyramid)
- Common Core State Standards: Grade 5, volume = length × width × height (5.MD.C.5b)
- Common Core State Standards: Grade 8, volumes of cones, cylinders and spheres (8.G.C.9)
- NIST Handbook 44 (2026): Appendix C, General Tables of Units of Measurement (gallon = 231 cubic inches)