Volume Word Problems (With Solutions)

Last updated: July 21, 2026 · Try each problem, then open the solution to check

How to approach any volume word problem: identify the shape, convert every measurement to one unit, pick the formula, substitute, then read the question again to give the answer in the units it asks for. That last step — the unit the answer needs — is where most marks are lost.

Problem 1 — Shipping crate

A shipping crate measures 1.5 m long, 0.8 m wide and 1.2 m tall. What is its volume?

Show solution

It is a box, so V = l × w × h.

V = 1.5 × 0.8 × 1.2 = 1.44 m³

Check it on the box calculator.

Problem 2 — Water butt

A cylindrical water butt has a radius of 0.5 m and a height of 1.5 m. How many litres does it hold when full?

Show solution

Cylinder: V = πr²h.

V = π × 0.5² × 1.5 = π × 0.25 × 1.5 = 1.178 m³

Convert to litres (× 1,000): ≈ 1,178 litres.

Problem 3 — Pile of sand

Sand is tipped into a cone-shaped pile 3 m across the base and 1.2 m high. What volume of sand is there?

Show solution

The base diameter is 3 m, so the radius is 1.5 m. Cone: V = ⅓πr²h.

V = ⅓ × π × 1.5² × 1.2 = ⅓ × π × 2.25 × 1.2 = 2.83 m³

Compare with the cone calculator or, for delivery, the sand calculator.

Problem 4 — Beach ball

A beach ball has a radius of 20 cm. What is its volume in litres?

Show solution

Sphere: V = (4/3)πr³.

V = (4/3) × π × 20³ = (4/3) × π × 8,000 = 33,510 cm³

Since 1,000 cm³ = 1 litre, that is ≈ 33.5 litres.

Problem 5 — Swimming pool

A rectangular pool is 10 m long, 4 m wide and a uniform 1.5 m deep. How many litres, and roughly how many US gallons, does it hold?

Show solution

Box: V = l × w × h.

V = 10 × 4 × 1.5 = 60 m³ = 60,000 litres

In US gallons (× 264.17): ≈ 15,850 gallons. The pool calculator handles sloping floors too.

Problem 6 — Grain silo (combined shape)

A silo is a cylinder 4 m in diameter and 6 m tall, topped by a cone 1.5 m high on the same base. Find the total volume.

Show solution

Radius = 2 m. Work out the two parts and add them.

Cylinder: π × 2² × 6 = 75.40 m³
Cone: ⅓ × π × 2² × 1.5 = 6.28 m³
Total = 75.40 + 6.28 = 81.68 m³

Splitting into parts is the key trick for any combined or irregular shape.

Common pitfalls

  • Diameter given, not radius. Halve it before using any πr² formula — problems 3 and 6 both do this deliberately.
  • Wrong final unit. The question may want litres or gallons even though you calculated in cubic metres. Always convert at the end.
  • Mixed units. If one measurement is in cm and another in m, convert first.

Frequently asked questions

How do you solve a volume word problem?

Identify the shape, note the measurements and convert them to one unit, choose the matching formula, substitute the numbers, then convert the answer to the units the question asks for. Reading carefully for the required unit is where most marks are lost.

How do you find the volume of a combined shape?

Split it into simple parts — for example a silo is a cylinder plus a cone — calculate each part separately, and add them together.

How do you convert cubic metres to litres in a word problem?

Multiply by 1,000. One cubic metre equals 1,000 litres, so 2.5 m³ is 2,500 litres.

Last updated: July 21, 2026 · Accuracy policy