Primary 5 Volume Study Guide
Primary 5 volume in five short steps: count unit cubes layer by layer, find the volume of a cuboid, read a cuboid on dot paper, change litres to cm³, then follow water from one tank to another.
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What is volume, and how do you measure it with unit cubes?
Volume is the number of unit cubes that fill a solid.
A unit cube is 1 unit along every edge. When the unit is 1 cm, each cube is 1 cubic centimetre, written 1 cm³; when it is 1 m, each cube is 1 m³. To find a volume, your child counts the cubes, and soon learns a quicker count: the cubes in one layer, times the number of layers.
In this chapter, your child learns to:
- build solids with unit cubes and count every cube, hidden ones too;
- find the volume of a cube or a cuboid in cubic units, cm³ or m³;
- read and draw cubes and cuboids on isometric dot paper;
- write litres and millilitres as cubic centimetres;
- find the water in a tank, and what happens when it is poured into another.
Step 1
Building solids with unit cubes
Count one layer at a time, from the bottom up. Every cube in a solid stands on the floor or on another cube, because nothing floats. So the bottom layer has one cube under each square of the top view, even where no face of that cube can be seen. Count the bottom layer, then each layer above it, and add. A view is a flat shape: it shows where the cubes stand, not how many there are.
The top view of a solid of unit cubes is 6 squares. Four of its columns are 1 cube tall, and the other two are 3 cubes tall. How many unit cubes are in the solid?
Step 2
Volume of a cube and cuboid
The volume is the floor of squares times the number of layers. Start every answer with the line volume = length × breadth × height. The length times the breadth is the base area, the squares covering the floor. The height is how many layers stand on it. A cube has three equal edges, so its volume is edge × edge × edge. For two boxes joined together, find each volume and add them. Measured in centimetres the answer is in cm³; in metres, in m³.
A cube has edges of 5 cm. Find its volume.
Step 3
Cubes and cuboids on isometric dot paper
Count the steps between the dots, not the dots. On isometric dot paper, each step from one dot to the next along an edge is 1 unit, so an edge that passes 6 dots is 5 units long. Start at the lowest vertex. One edge goes right and up, one goes left and up, and one goes straight up: the length, the breadth and the height. The three edges that meet at the back corner are hidden, so they are drawn with dashes.
On isometric dot paper, a cuboid's length edge passes 4 dots, its breadth edge 3 dots and its height edge 5 dots. How many unit cubes build the cuboid?
Step 4
Litres, millilitres and cubic centimetres
1 ℓ = 1000 ml, and every millilitre is 1 cm³. A cube 1 cm along every edge holds exactly 1 ml of water. A box 10 cm along every edge is 10 layers of 100 such cubes, so it holds 1000 cm³, which is 1 litre. Litres and millilitres cannot be added as they stand, so change the litres to millilitres first. The number of millilitres is then the number of cubic centimetres.
This jug is marked at 1 ℓ and 2 ℓ, with 4 equal gaps for each litre.
A kettle holds 2 ℓ 9 ml of water. Give the volume of that water in cubic centimetres.
Step 5
Water in a tank and pouring between containers
The same water has the same volume in any tank. The water in a tank is a cuboid of its own: the base area times the depth of the water. The tank's height only says how much the tank can hold. When water is poured into another tank, find its volume first. Compare it with the space in the new tank to see how much overflows or how much room is left, or divide it by the new base area to find the new water level.
Tank A has a base 25 cm by 12 cm and is 20 cm high. It holds water 10 cm deep. All the water is poured into empty Tank B, which has a base 20 cm by 10 cm and is 12 cm high. How much water overflows?
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A tank is 30 cm long and 20 cm wide. It holds 4.8 ℓ of water. How deep is the water?
Primary 5 volume questions, worked step by stepRead each question and try it on paper first. Open the hint if you are stuck, then reveal one line at a time.
A solid is built from unit cubes in 3 layers, like a staircase. The bottom layer is 4 cubes long and 3 cubes deep. The middle layer is 4 cubes long and 2 deep. The top layer is 4 cubes long and 1 deep. How many unit cubes are used?
- bottom layer = 4 × 3 = 12
- middle layer = 4 × 2 = 8
- top layer = 4 × 1 = 4
- total = 12 + 8 + 4 = 24
A storeroom is shaped like a cuboid 5 m long, 4 m wide and 3 m high. Find its volume.
- volume = length × breadth × height
- base area = 5 × 4 = 20 m²
- volume = 20 × 3 = 60 m³
A solid is made of two rectangular boxes joined together. The lower box is 9 cm long, 5 cm wide and 3 cm high. The upper box is 4 cm long, 5 cm wide and 2 cm high. Find the volume of the solid.
- volume = length × breadth × height, for each box
- lower box = 9 × 5 × 3 = 135 cm³
- upper box = 4 × 5 × 2 = 40 cm³
- volume of the solid = 135 + 40 = 175 cm³
A jug holds 2 ℓ 85 ml of water. A bottle holds 1.35 ℓ. How much more water does the jug hold than the bottle? Give your answer in cubic centimetres.
- 1 ℓ = 1000 ml = 1000 cm³
- jug = 2000 + 85 = 2085 ml
- bottle = 1.35 × 1000 = 1350 ml
- difference = 2085 − 1350 = 735 ml = 735 cm³
Tank A is 30 cm long, 20 cm wide and 25 cm high. It holds water 15 cm deep. Water from Tank A is poured into an empty tank, Tank B, until Tank B is full. Tank B is 20 cm long, 15 cm wide and 20 cm high. How deep is the water left in Tank A?
- water in Tank A = 30 × 20 × 15 = 9000 cm³
- water to fill Tank B = 20 × 15 × 20 = 6000 cm³
- water left in Tank A = 9000 − 6000 = 3000 cm³
- base area of Tank A = 30 × 20 = 600 cm²
- depth of water left = 3000 ÷ 600 = 5 cm
Step 6
Check yourself
Five questions, one for each step. Each reply says where to practise next.
A solid has 3 layers of unit cubes. The bottom layer has 9 cubes, the middle layer 4 and the top layer 1. How many unit cubes are there?
Find the volume of a cube with edges of 6 cm.
On isometric dot paper, an edge of a cuboid passes 7 dots. How long is the edge?
Express 4 ℓ 8 ml in cubic centimetres.
A tank holds 5000 cm³ of water. All of it is poured into an empty tank that can hold 4200 cm³. How much water overflows?
Using this guide with your child. Take one step at a time. Before each tap, ask your child to say what will change: how many cubes a layer holds, or how many steps an edge has. The picture then shows whether they were right, which is more convincing than being told.
Small blocks, dice or sugar cubes make the first step real: build a solid, count it layer by layer, then lift a layer off to find the cube nobody could see. In the kitchen, a measuring jug shows that a litre is 1000 ml, and each of those millilitres is one cubic centimetre.
More study guides
P5 Volume lessons and practice
5 lesson videos and 37 questions across six subtopics, from Basic to Challenge, each with a worked solution.
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