Primary 6 · Measurement & Geometry

P6 volume of cube and cuboid

In P6, volume runs backwards. Your child is given the volume and finds a missing side, a cube's edge or a base area, also in compound solids made of two cuboids.

Taught in: Term 2
Syllabus: 3 skills
Usual slip: Dividing by 3

Updated 23 October 2026

What your child learns in P6 volume of cube and cuboid

Three skills, each with what it looks like on a worksheet.

Follows the latest (2026) MOE syllabus

See the syllabus wording

finding one dimension of a cuboid given its volume and the other dimensions
finding the length of one edge of a cube given its volume
finding the height of a cuboid given its volume and base area
finding the area of a face of a cuboid given its volume and one dimension
use of √ and ∛

A missing side from the volume

A missing side is the volume ÷ the other two sides, and a face's area is the volume ÷ the third side. 504 cm³ on a 9 cm by 8 cm base: 504 ÷ 72 = 7 cm tall.

504 cm³

A cube's edge from its volume

A cube's three edges are equal. So its edge is the number that multiplies by itself three times to make the volume. 27 unit cubes make a cube 3 long, because 3 × 3 × 3 = 27.

3 × 3 × 3 = 27

Square roots and cube roots

√49 = 7: a square face of 49 cm² has 7 cm sides. ∛64 = 4: a cube of 64 cm³ has 4 cm edges. Knowing 1, 8, 27, 64 and 125 by sight helps.

√49 = 7

Key facts and formulas

Term 2

Volume of a cuboid $V = l \times b \times h$ a cube: edge × edge × edge
Height of a cuboid $h = V \div \text{base area}$ Example360 cm³, base 40 cm² → $360 \div 40 =$ $9\,\text{cm}$
Area of a face $A = V \div h$ Example480 cm³, h = 6 cm → $480 \div 6 =$ $80\,\text{cm}^{2}$
Edge of a cube $\text{edge} = \sqrt[3]{V}$ Example343 cm³ → $\sqrt[3]{343} =$ $7\,\text{cm}$
Square root and cube root√ undoes squaring; ∛ undoes cubing $\sqrt{64} =$ $8$ $\sqrt[3]{64} =$ $4$

Words to know

Volume: The space a solid takes up, in cubic units such as cm³.
Base area: The area of the face a solid stands on, length × breadth.
Edge: A line where two faces of a solid meet.
Square root (√): The number that times itself gives this one. √49 = 7.
Cube root (∛): The number that times itself three times gives this one. ∛64 = 4.

The sentence that costs the mark

A cube has a volume of 216 cm³. Find the length of one edge.

216 cm³

What the working usually does

a third of216 cm³=72 cm

A cube has three equal edges, so dividing by 3 sounds like a reason. 72 is a clean number, and the working looks done.

What the question asked

∛216 cm³=6 cm

The edge is the number that times itself three times to make 216. 6 × 6 × 6 = 216, so each edge is 6 cm.

Both lines start from the right volume and neither has a sum wrong. Multiplying back is the check: an edge of 72 cm makes a cube of 373 248 cm³, nowhere near 216.

The same P6 volume of cube and cuboid question, worked properly

Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.

A block of cheese was cut across into blocks A (360 cm³) and B (600 cm³). B was 4 cm taller than A. Find the height of the whole block.

Step 1 of 5▌

Both blocks sit on the same base, so block B is bigger only because it is 4 cm taller. The extra volume is 600 − 360 = 240 cm³.
That extra 240 cm³ is a slice 4 cm tall, so the base area = 240 ÷ 4 = 60 cm². The 4 cm goes with the extra volume, not with a whole block.
The whole block of cheese has a volume of 360 + 600 = 960 cm³.
Height is volume divided by base area, so the height = 960 ÷ 60 = 16 cm.
So the height of the whole block of cheese is 16 cm.

Every question in StudyLah comes with a walkthrough like this one.

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Two quick P6 volume of cube and cuboid questions

Try them together, then tap to check.

Question 1

A rectangular tank has a square base and a height of 12 cm. Its shaded face has an area of 60 cm². Find the volume of the tank.

Show answer

Answer300 cm³. The shaded face's other side is 60 ÷ 12 = 5 cm. The base is square, so the volume is 5 × 5 × 12 = 300.

Question 2

One face of a cube covers an area of 121 cm². Find the volume of this cube.

Show answer

Answer1331 cm³. √121 = 11, so each edge is 11 cm, and the volume is 11 × 11 × 11 = 1331.

Helping at home

How to tell it has clicked

Ask for the edge of a cube of 64 cm³. An answer near 21 means the volume was divided by 3. The answer you want is 4, with the check said out loud: 4 × 4 × 4 = 64.

Give a cuboid's volume and its base area, and ask for the height. Dividing by one side of the base misses that the base area already holds two.

Try this tonight

Build a cube from sugar cubes or dice, 2 by 2 by 2, then 3 by 3 by 3. Ask how many it took each time, and how long each edge is.

Then turn it round: if a cube used 64, how long is its edge?

Before and after P6 volume of cube and cuboid

Builds on
Primary 5 Volume of Cube and Cuboid
Builds cuboids from unit cubes
You are here
Primary 6 Volume of Cube and Cuboid
Works backwards from a volume

In the PSLE's hardest questions

2026 Paper 2 Question 13: the painted cube cut in two

More in Primary 6

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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