Quick start
- Enter the radius r. For the cube, this value is used as the side length.
- Enter the height h for the cylinder and cone.
- Read the volume and surface area of each shape.
Formulas
| Shape | Volume | Surface area |
|---|---|---|
| Sphere | 4/3 πr³ | 4πr² |
| Cylinder | πr²h | 2πr² + 2πrh |
| Cone | 1/3 πr²h | πr² + πr·√(r² + h²) |
| Cube | s³ | 6s² |
Example: a water tank
A cylindrical tank has a radius of 0.5 m and a height of 1.2 m. Its volume is π × 0.25 × 1.2 ≈ 0.942 m³. One cubic metre holds 1,000 litres, so the tank holds about 942 litres.
A neat relationship
A cone holds exactly one third of the cylinder with the same base and height. A sphere holds two thirds of the cylinder that just fits around it. Archimedes was so pleased with this result that he asked for it on his tombstone.
Common questions
What is slant height?
The distance from the tip of a cone down its side to the edge of the base: √(r² + h²).
How do I turn cm³ into litres?
Divide by 1,000. 1,000 cm³ = 1 litre.
Does the surface area include the ends?
Yes, for the cylinder and cone the flat base or bases are included.