METRONMETHOD. REASON. LEARN.
Measurement · 12 min

Volume

Containers, storage boxes and water tanks need three dimensions. Surface area alone cannot tell you what they hold.

01Why this matters

Containers, storage boxes and water tanks need three dimensions. Surface area alone cannot tell you what they hold.

02See it

2 m1 m0.5 m
A rectangular tank: base area 2 m², stacked through a height of 0.5 m, gives 1 m³. Schematic, not to scale.
2 m length1 m width0.5 m height1 m³ = 1,000 L
Read left to right: 2 m length → 1 m width → 0.5 m height → 1 m³ = 1,000 L. Each panel connects one part of the example.

03Understand it

Volume is the amount of three-dimensional space an object or substance occupies, measured in cubic units.

For a rectangular prism, multiply length, width and height. Think of the base area covered by layers: each metre of height adds another base-sized layer of cubic metres. Capacity is the volume a container can hold internally. One litre equals 1,000 cm³, or 0.001 m³.

04Guided example

A tank’s internal dimensions are 2 m by 1 m by 0.5 m. What is its capacity?

  1. Find the base area: 2 × 1 = 2 m².
  2. Multiply by height: 2 × 0.5 = 1 m³.
  3. Convert to litres: 1 m³ = 1,000 L. The theoretical capacity is 1,000 L.

05Try it

Find volume for a 3 m by 2 m by 4 m prism.
A little hint

Multiply all three dimensions.

06Practise it

Convert 2 m³ to litres.
A little hint

Each cubic metre holds 1,000 litres.

Convert 5,000 cm³ to litres.
A little hint

Each litre is 1,000 cm³.

07Use it in the real world

A 30 cm by 20 cm by 10 cm box has volume 6,000 cm³, equivalent to 6 L. Its useful capacity may be smaller if corners are rounded.

Go a little deeper

When all lengths triple, volume grows by 3³ = 27. This explains why a small increase in container dimensions can produce a much larger increase in capacity.

08Quick check

A prism has base area 6 m² and height 2 m. Volume?
A little hint

Multiply the base area by height.

09Summary

Volume is the amount of three-dimensional space an object or substance occupies, measured in cubic units. Convert to litres: 1 m³ = 1,000 L. The theoretical capacity is 1,000 L.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

V = lwh

V is volume in m³ when l, w and h are all in metres.

h = V/(lw), for non-zero l and w

Find this in the formula library →