Quick answer: A cylinder with radius 3 cm and height 10 cm holds π × 3² × 10 = 282.743339 cm³, which is 0.2827 litres.
How it's calculated
Prisms and cylinders: volume = base area × height, so a box is l × w × h and a cylinder is πr²h. Cones and pyramids hold one third of the matching cylinder or prism: 1/3 × πr²h and 1/3 × s²h.
Sphere: 4/3 × πr³; a hemisphere is half of that. A capsule is a cylinder with a hemisphere at each end: πr²h + 4/3 × πr³, where h is the length of the straight part.
Volume is in cubic units. One litre is 1,000 cm³ (a cube 10 cm on each side), and 1 m³ = 1,000 litres, which is how water tanks are usually sized in the Gulf.
Worked examples
- Cylinder r = 3 cm, h = 10 cm: π × 9 × 10 = 282.743339 cm³ = 0.2827 L
- Sphere r = 3: 4/3 × π × 27 = 113.097336
- Box 10 × 5 × 10 cm: 500 cm³ = 0.5 L
Frequently asked questions
How many litres does a tank hold?
Measure it in metres, pick m as the unit and read the capacity: each cubic metre is 1,000 litres.
Why is a cone one third of a cylinder?
It is a classical result (proved by Eudoxus and Archimedes, and by integration today): any cone or pyramid has one third the volume of the prism or cylinder with the same base and height.
How do I get the paint or wrapping area instead?
That is the surface area; use the surface area calculator.
What's the volume of a cylinder with a 3 cm radius and 10 cm height?
About 282.7 cm³, a little over a quarter of a litre.
How do I work out a room's volume for an air purifier?
Multiply length by width by ceiling height. A 5 × 4 m room with a 3 m ceiling is 60 m³.
How much does a round water tank hold?
A tank 1.2 m across and 1.5 m tall holds about 1.7 m³, roughly 1,700 litres. Use the cylinder shape with a radius of 0.6 m.