Volume formulas: cube, box, cylinder, cone and sphere
Most volume formulas follow one idea: the area of the base multiplied by the height. Cones and spheres add one simple factor, and units do the rest of the work.
Cube, box and cylinder
cube: V = a³
box: V = length × width × height
cylinder: V = π × r² × h
Example: a cylinder with r = 3 and h = 10
- r² = 9
- V = π × 9 × 10 = 90π
V ≈ 282.7
Cone and sphere
cone: V = π × r² × h ÷ 3
sphere: V = 4/3 × π × r³
Example: a cone with r = 3 and h = 10
- π × 9 × 10 = 90π
- 90π ÷ 3 = 30π
V ≈ 94.2, a third of the matching cylinder
Example: a sphere with r = 3
- r³ = 27
- V = 4/3 × π × 27 = 36π
V ≈ 113.1
Units and litres
- 1 litre = 1 dm³ = 1,000 cm³.
- 1 m³ = 1,000 litres.
- Convert every length into the same unit before calculating.
Volume grows with the cube of size: doubling every side of a cube multiplies its volume by 8.
Common pitfalls
- Using the diameter instead of the radius.
- Forgetting to divide by 3 for a cone.
- Mixing centimetres and metres in the same calculation.
Worked exercises
Try to find the answer first, then open the solution.
What is the volume of a box measuring 8 × 5 × 3?
Show the solution
- 8 × 5 = 40
- 40 × 3 = 120
Answer: 120
What is the volume of a cylinder with r = 2 and h = 7?
Show the solution
- π × 4 × 7 = 28π
Answer: 28π ≈ 88.0
What is the volume of a sphere with r = 6?
Show the solution
- r³ = 216
- 4/3 × π × 216 = 288π
Answer: 288π ≈ 904.8