The idea in brief. Cut one layer, a centimetre thick, off the box and set it beside it. That layer is a floor of centimetre squares, count them, 8 along and 5 back, and that is the base area. The box is 3 cm high, so it is 3 of those floors. So length times breadth times height IS the floor, times the layers.
Lesson video, with the working
Volume of a cuboid
2 min 45 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
A box has a length of 8 cm, a breadth of 5 cm and a height of 3 cm. Find the volume of the box.
The volume of the box is 120 cm³.
Ans: 120 cm³
Example 1
A solid is made from two rectangular boxes joined together, as shown. The lower box has a length of 10 cm, a breadth of 6 cm and a height of 4 cm. The upper box has a length of 5 cm, a breadth of 6 cm and a height of 3 cm. Find the volume of the solid.
Total volume of two boxes = 240 + 90 = 330 cm³
Ans: 330 cm³
How to solve it
Think of volume as layers one centimetre thick. One layer is the floor, the base area.
Count the floor: 8 squares along the front and 5 rows back, which is 8 times 5, or 40 squares.
Stack the floors: volume is length times breadth times height, so 40 times 3 is 120 cubic centimetres.
For two boxes joined, find each volume on its own. The lower box is 10 times 6 times 4, which is 240.
The upper box is 5 times 6 times 3, which is 90. Add them: 240 plus 90 is 330 cubic centimetres.
Two boxes joined are two volumes added. And the upper box is floors of squares too. Its floor is 5 by 6, and it is 3 floors high.
Practice questions with worked solutions
Question 1 is free to try. The other 6 open in the free trial, each with its full working.
How do you find the volume of cuboids and composite solids in P6?
Volume is the number of unit cubes that fill a solid.
What your child learns here
Volume is the number of unit cubes that fill a solid. This page treats a cuboid as layers, one base area thick, and extends that to solids made of two boxes. The rule itself is an outcome from earlier years, and every Primary 6 volume outcome runs it backwards, so it needs to be secure.
See volume as layers: one layer is the base area, and the volume is that times the number of layers.
Find the volume of a cuboid as length times breadth times height, in cubic centimetres or cubic metres.
Spot a third dimension given in words, such as deep, tall or high, rather than as a label.
Split a composite solid into two cuboids and add, or take a cut-off piece from a whole block.
Find how many more unit cubes fill a box: the box's total minus the cubes already inside.
Does the answer make sense?
A volume carries cubic units, and for two boxes joined it must be more than the bigger box alone but less than one block that would wrap round both. When slabs are trimmed off, or cubes already sit inside, your child's answer must be less than the full block.
How to practise these questions
The Basic questions train volume as one layer of cubes times the number of layers. Intermediate questions add solids made of two boxes, where each box is measured separately. Challenge questions read lengths off a net, or take a cut-out away from a block. If the layers of a cuboid do not add up, read the written step-by-step solution together.
Questions parents ask
What is the formula for the volume of a cuboid? Volume equals length times breadth times height, which is the same as base area times height. The answer is in cubic units, such as cubic centimetres.
How do you find the volume of a composite solid? Split it into cuboids that do not overlap, find each volume, and add. If a piece has been cut away from a block, find the whole block and subtract the piece.
Is volume of a cuboid taught in P5 or P6? The volume of a cube or cuboid is a Primary 5 outcome in the MOE syllabus. Primary 6 extends it: finding a missing dimension, an edge, a height or the area of a face from a given volume.
