Which formula gives the volume of each solid?
Choose a shape, enter its dimensions in metres and calculate. Volume is reported in m³; total surface area and base area are in m². These measure different things.
Formula
1 m³ = 1,000 L; 1 cm = 0.01 m
| Solid | Volume |
|---|---|
| Rectangular prism | L × W × H |
| Cube | a³ |
| Cylinder | π × r² × H |
| Sphere | 4 × π × r³ ÷ 3 |
| Cone | π × r² × H ÷ 3 |
| Square pyramid | a² × H ÷ 3 |
| Triangular prism | (b × h ÷ 2) × L |
| Hemisphere | 2 × π × r³ ÷ 3 |
L: length; W: width; H: height; a: side of the square; r: radius. For a triangular prism, b and h are the triangle’s base and perpendicular height, and L is the prism length. π is approximately 3.14159.
Worked example
A rectangular prism measuring 5 × 4 × 3 m has a volume of 60 m³.
Its total surface area is 2 × (5 × 4 + 5 × 3 + 4 × 3) = 94 m². The 60 m³ volume is not an area to coat.
Assumptions and limits
- These are ideal shapes. Wall thickness, openings and irregularities are not subtracted. Use internal dimensions when estimating capacity.
- The cylinder and prisms are right solids; the cone and pyramid have centred apexes. Triangular-prism surface area assumes a right-triangle base with b and h as perpendicular sides. Hemisphere surface area includes the flat circular base.
Common questions
Can I enter dimensions in centimetres?
The fields use metres. Divide centimetres by 100 first: 50 cm is entered as 0.5 m. Convert every dimension, not only the first one.
Do I enter radius or diameter?
The sphere, hemisphere, cylinder and cone modes ask for radius. It is half the diameter: for a diameter of 2 m, enter a radius of 1 m.