Worked Volume Examples

Last updated: July 21, 2026 · Every example shows the formula, the substitution and the answer

Each example below follows the same three steps: write the formula, substitute the numbers, simplify. That is exactly how to earn full marks in an exam and how to catch your own mistakes. Every shape links to a calculator that shows the same working automatically.

Example 1 — Cube

Find the volume of a cube with edge 4 cm.

V = a³ = 4³ = 4 × 4 × 4 = 64 cm³

Try your own numbers on the cube calculator.

Example 2 — Rectangular box

A box measures 5 cm × 4 cm × 3 cm.

V = l × w × h = 5 × 4 × 3 = 60 cm³

Example 3 — Cylinder

A can has radius 3 cm and height 10 cm.

V = π r² h = π × 3² × 10 = π × 9 × 10 = 282.7 cm³

That is about 283 mL — a standard soft-drink can. See the cylinder calculator.

Example 4 — Cone

An ice-cream cone has base radius 2 cm and height 9 cm.

V = ⅓ π r² h = ⅓ × π × 2² × 9 = ⅓ × π × 36 = 37.7 cm³

Example 5 — Sphere

A ball has radius 5 cm.

V = (4/3) π r³ = (4/3) × π × 5³ = (4/3) × π × 125 = 523.6 cm³

Example 6 — Square pyramid

A pyramid has a 6 cm square base and height 10 cm.

V = ⅓ × base area × h = ⅓ × (6 × 6) × 10 = ⅓ × 36 × 10 = 120 cm³

Example 7 — A real-world mix

How much water fills a cylindrical tank 1.2 m across and 2 m tall?

Radius = 1.2 ÷ 2 = 0.6 m. Then:

V = π × 0.6² × 2 = π × 0.36 × 2 = 2.262 m³ = 2,262 litres

Because 1 m³ = 1,000 L, the litres follow immediately. The water tank calculator does this in one step.

Ready to practise?

These examples give you the pattern; the volume word problems page turns them into full questions with answers to check against.

Frequently asked questions

What is an example of calculating volume?

For a box 5 cm long, 4 cm wide and 3 cm high, volume = 5 × 4 × 3 = 60 cubic centimetres. You multiply the three dimensions together, keeping them all in the same unit.

How do you show working for a volume calculation?

Write the formula, substitute the numbers, then simplify. For a cylinder: V = πr²h = π × 3² × 10 = π × 9 × 10 = 282.7 cm³. Showing each step earns full marks and makes errors easy to spot.

What is the volume of a sphere with radius 5 cm?

V = (4/3)π × 5³ = (4/3)π × 125 = 523.6 cubic centimetres.

Last updated: July 21, 2026 · Accuracy policy