How to use
- Choose the solid.
- Enter the dimensions shown in the diagram, all in the same unit.
- The volume and surface area appear on the right, with the volume formula below.
Options explained
- Unit
- Only changes the unit shown — cubic units for volume, square units for surface area. Nothing is converted.
- Surface area
- For cylinders, cones and frustums the surface area includes the flat ends; for a hemisphere it includes the curved surface and the base circle.
- Capacity
- 1 litre = 1,000 cm³ = 1 dm³, and 1 US gallon ≈ 231 in³.
Examples
| Solid | Dimensions | Volume | Surface area |
|---|---|---|---|
| Cylinder | r = 5, h = 6 | 471.2389 | 345.5752 |
| Cone | r = 3, h = 4 | 37.6991 | 75.3982 |
| Sphere | r = 5 | 523.5988 | 314.1593 |
Frequently asked questions
How do I find the volume of a cylinder?
Volume = π × radius² × height. A cylinder with a 5 cm radius and 6 cm height holds about 471.24 cm³, or about 0.47 litres.
Why is a cone's volume divided by 3?
A cone has exactly one third of the volume of a cylinder with the same base and height, so V = π × r² × h ÷ 3. A cone with radius 3 and height 4 has a volume of about 37.70.
What are the formulas for a sphere?
Volume = 4/3 × π × r³ and surface area = 4 × π × r². A sphere of radius 5 has a volume of about 523.60 and a surface area of about 314.16.
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