Volume calculator for 3D shapes with working

• Cuboid: 5 cm × 4 cm × 3 cm. Volume $= 60$ cm³.
• Cylinder: radius 3 cm, height 10 cm. $\pi \times 3^2 \times 10 = 90\pi \approx 282.7$ cm³.
• Cone: radius 3 cm, height 4 cm. $\tfrac{1}{3} \times \pi \times 9 \times 4 = 12\pi \approx 37.7$ cm³.
• Sphere: radius 3 cm. $\tfrac{4}{3} \times \pi \times 27 = 36\pi \approx 113.1$ cm³.

A prism has the same cross-section all the way through: cuboids, cylinders and triangular prisms are all prisms. Its volume is the area of the cross-section × the length. Find the cross-section's area first (our area calculator helps), then multiply. A triangular prism with a cross-section of 20 cm² and a length of 8 cm has a volume of 160 cm³.

A cone fills exactly a third of the cylinder with the same base and height, and a pyramid a third of the prism. So the cone in the example (12π) is a third of the cylinder with radius 3 cm and height 4 cm (36π). Use the perpendicular height, from the tip straight down to the base, not the slant height.

Volume is measured in cubic units: $1 \text{ m}^3 = 100^3 = 1000000$ cm³. For liquids, 1 litre = 1,000 cm³ and 1 ml = 1 cm³. A cylinder of volume 282.7 cm³ holds about 0.28 litres.

• Using the diameter instead of the radius.
• Forgetting the $\tfrac{1}{3}$ for cones and pyramids.
• Cubing when you should square (or the other way round): $r^2$ in a cylinder, $r^3$ in a sphere.
• Using a slant height for a cone's volume.

Practise with our volume and surface area questions.

• Formulae for the volume of a cone, sphere and pyramid are usually given in GCSE and IGCSE exams; prisms and cylinders you should know.
• For a hemisphere, halve the sphere: $\tfrac{2}{3}\pi r^3$.
• Composite solids: add or subtract the volumes of the parts, such as a cone on top of a cylinder.
• Keep $\pi$ in your working until the end to avoid rounding errors.