Find unknown dimensions of a cube or cuboid

What you will learn

• Find unknown dimensions of a cube or cuboid

Models used: number sentences, stories, tables.

Before you start

• Convert between litres, millilitres and cm³

Recover the missing layers

The cuboid contains 36 cubes. Its base is 4 by 3, so each layer contains 12.

1. Count cubes across a layer, then count the layers. Some cubes are hidden.

   The cuboid contains 36 cubes. Its base is 4 by 3, so each layer contains 12.

   4 × 3 = 12 cubes per layer

   Width 4, height 1, depth 3

2. Count cubes across a layer, then count the layers. Some cubes are hidden.

   Two layers contain 24 cubes. We need one more layer to reach 36.

   Width 4, height 2, depth 3

3. Count cubes across a layer, then count the layers. Some cubes are hidden.

   There are three layers, so the height is 3 units.

   height = 36 ÷ 12 = 3

   Width 4, height 3, depth 3

Worked example: A new example, together

A cuboid has volume 16 cm³ and a base 4 cm by 2 cm. Find its height.

1. All dimensions refer to the same unit. Read each value with the heading above its column.

   Work out the known face first, then divide the volume by it.

   Equal layers connect base area and height with total volume.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	?

2. All dimensions refer to the same unit. Read each value with the heading above its column.

   Volume = base area × height.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	?

   A cuboid has volume 16 cm³ and a base 4 cm by 2 cm. Find its height.

   2 cm

3. All dimensions refer to the same unit. Read each value with the heading above its column.

   Base area = 4 × 2 = 8.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	?

4. All dimensions refer to the same unit. Read each value with the heading above its column.

   Height = 16 ÷ 8 = 2 cm.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	?

5. All dimensions refer to the same unit. Read each value with the heading above its column.

   Check the result against the question we started with.

   8 × 2 = 16.

   We found 2 cm. Equal layers connect base area and height with total volume.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	?

Common mistakes to discuss

• Dividing by one edge only. Volume is the product of three lengths. With volume 60 cm³ on a 5 cm by 4 cm base, the height is 60 ÷ 20 = 3 cm.

Check your understanding

• Find unknown dimensions of a cube or cuboid
• work back from a volume to a missing dimension
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.