Volume and surface area
Volume is how much a shape can hold. Choose the shape and enter the measurements — the answer also comes in litres, so you can see how much water it can hold.
The explanation is shown. Quick: box, cube, cylinder, cone and sphere. Advanced: also pyramid, prism, tube and truncated cone — and the volume in every unit and at other dimensions.
Your numbers
Answer
Volume
6,000cm³
Volume in litres
6l
Surface
2,200cm²
How to work it out
- 1V = l · b · h = 30 · 20 · 10 = 6,000 cm³
- 2O = 2 · (l·b + l·h + b·h) = 2 · (600 + 300 + 200) = 2,200 cm²
The formula
V = l · b · h
The base area times the height.
1 litre = 1 dm³ = 1,000 cm³. 1 m³ = 1,000 litres.
In depth: more numbers and “what if”
The volume in every unit
| Unit | Volume |
|---|---|
| mm³ | 6,000,000 |
| cm³ | 6,000 |
| dm³ = litre | 6 |
| m³ | 0.006 |
What if every measurement is multiplied by k?
| k | Volume | Surface | Volume multiplied by |
|---|---|---|---|
| 0.5 | 750 cm³ | 550 cm² | 0.125 |
| 0.9 | 4,374 cm³ | 1,782 cm² | 0.729 |
| 1 | 6,000 cm³ | 2,200 cm² | 1 |
| 1.1 | 7,986 cm³ | 2,662 cm² | 1.331 |
| 2 | 48,000 cm³ | 8,800 cm² | 8 |
The volume grows with k³ and the surface area with k²: dimensions twice as large give eight times the volume.
More: Geometry
- PythagorasFind the missing side, set out a right angle, check whether a room is square, and find the space diagonal.
- Area and perimeterRectangle, triangle, trapezium, circle and composite shapes — area and perimeter.
- The circleRadius, circumference and area from one measurement — plus sector, annulus, chord and rise.
- Right triangleSine, cosine and tangent: all sides and angles from two known values.
- AnglesThe third angle in a triangle and the angle sum of a polygon.
- Points in the coordinate systemDistance, midpoint and the line between two points — drawn in.
- Similar figuresScale factor and missing sides — area is multiplied by k², volume by k³.
- Any triangleThe sine and cosine rules: find the rest from SSS, SAS, ASA or SSA.
- TransformationsReflect, rotate and translate a figure on a coordinate grid — before and after.