Primary 6 · Mathematics
P6 volume of cube and cuboid
The hardest compound solids do not hide the method, they hide a measurement. One length the picture never prints, and the tempting number sitting right next to it. Here it is.
- Level
- P6
- Usually taught
- Term 2
- Covers
- 1 concept
What changes at P6
At Primary 6, volume stops being one block. A compound solid is two or more cuboids joined, an L, a T, a step. The method never changes: split into cuboids, find each with length × width × height, then add. There is no special formula; hunting for one is the first wrong turn.
What P6 adds is that the picture stops handing you every number. One block's height is left off, and you work it out from the sizes around it. Finding it is the skill tested.
The sentence that costs the mark
The L-shaped solid below is made of two blocks. Find the volume of the top block.
What the working usually does
top block = 8 × 7 ×10=560 cm³
The 10 cm is printed on the figure, so it is the easy number to reach for. But it is the height of the whole left side, not the top block.
What the question asked
top block = 8 × 7 ×4=224 cm³
The top block only rises from the 6 cm bottom up to the 10 cm top, so its height is 10 − 6 = 4 cm. That number is never printed.
Every other figure in the wrong line is correct, and 560 looks like a real volume. That is what makes it hard to catch over a child's shoulder: the mistake is one measurement, and it is the only one the picture asks you to work out rather than read.
The same question, worked properly
Split into two cuboids
bottom block + top blockImagine sawing the L into a bottom block and a top block. This is the whole method for any compound solid, and it needs no new formula.
Find the bottom block
bottom = 15 × 7 × 6 = 630 cm³All three of its measurements are printed on the figure, so this one is direct.
Work out the missing height
top height = 10 − 6 = 4 cmThis is the step that fails. The top block's height is not printed. The left side is 10 cm all the way up, and the bottom block takes the first 6 cm, so the top block is the 4 cm that is left. This is the line the marks turn on.
Find the top block
top = 8 × 7 × 4 = 224 cm³Now every measurement is known, so it is length × width × height like any cuboid.
How can you tell it has clicked?
You do not need to do the maths to check this. Ask one question about the working: "did every number come off the picture, or did you work one out?"
A child who understands points at the height and says they found it, 10 take away 6. A child who read all three numbers straight off the figure has walked into the trap, and will walk into it again on every composite figure in the paper.
One thing to try tonight
Stack two boxes of different sizes, a big one flat and a smaller one on top at one end, so the whole thing makes an L. Ask your child which measurements they would need to find its volume, and which ones they cannot read without a ruler.
That is the exam skill in one move: knowing which number is missing before reaching for the calculator. The blocks make it obvious in a way the flat picture hides.
What your child will meet in this topic
- Compound Volume
Most Singapore schools introduce this in Term 2, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
The same split-find-add habit runs through every composite-figure question, and into the subtraction version, a big cuboid with a smaller one cut out, where the missing piece is what you take away instead of add.
In secondary school the pieces become prisms and cylinders, but the move is identical: break the shape into parts you know, find each, combine. A child who splits cleanly now carries that straight through.
The same topic in other years
It comes back each year and gets harder, so it helps to see what came before and what is coming.
More in Primary 6
Other topics in the same year, so you can see what sits either side of this one.
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.