Primary 6 Volume Study Guide
Primary 6 volume in five short steps, each built on the same picture: a floor of squares, stacked in layers. Every step has a drawing to try, and worked examples follow.
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What is volume, and how do you find the volume of a cuboid?
A volume is a floor of squares, stacked in layers.
Fill a box with 1-cm cubes. The bottom layer covers the floor: its number of cubes is the base area in square centimetres. The height says how many layers stand on that floor. So the volume is the base area times the height, measured in cubic centimetres (cm³).
In this chapter, your child learns to:
- find the volume of a cuboid, and of a solid made of two cuboids;
- work back from a volume to a length, a height, a base area or the edge of a cube;
- count the unit cubes in a solid, and draw its front, side and top views;
- change litres and millilitres to cubic centimetres;
- find a water level, and the new level after water is poured into another tank.
One layer: 4 × 3 = 12 cubes. The floor, the base area, is 12 cm².
The box is 3 cm high, so 3 layers stand on that floor.
Volume = base area × height = 12 × 3 = 36 cm³
Step 1
Volume of a cuboid and of joined solids
Find the floor, then count the layers standing on it. Write volume = length × breadth × height first, then put in the numbers. The length times the breadth is the base area, the cubes in one layer. The height is the number of layers. A solid made of two cuboids has two volumes: find each one, then add them.
Tap + or −
Two cuboids joined? Find each volume this way, then add.
A solid is made of two cuboids. The bottom one is 8 cm by 5 cm by 3 cm. The top one is 4 cm by 5 cm by 2 cm. Find the volume of the solid.
Step 2
Finding a missing length, height or edge from the volume
Divide the volume by the base area, and the height is left. Start from the same first line, volume = length × breadth × height. Write the base area on its own line, then divide the volume by it. Keep the units: cm³ ÷ cm² leaves cm, a length. A cube has three equal edges, so its edge is the cube root of its volume: ∛343 = 7, because 7 × 7 × 7 = 343.
A cuboid has a volume of 960 cm³. Its base is 12 cm by 8 cm. Find its height.
Tap Next step
A tank has a square base and a height of 10 cm. Its volume is 640 cm³. Find the length of one side of the base.
Step 3
Counting unit cubes from front, side and top views
Count layer by layer from the bottom, hidden cubes too. A view is the solid drawn flat from one side, with one square for each column seen from there. A view is a shape, so it does not tell you the number of cubes. To count, start with the bottom layer. Every cube in a higher layer stands on a cube below it, even when no face of that cube can be seen.
Tap a view
The top view of a solid is 5 squares. Every column of the solid is 2 cubes tall. How many unit cubes are in the solid?
Step 4
Converting litres and millilitres to cubic centimetres
1 ℓ = 1000 ml = 1000 cm³, so every millilitre is a cubic centimetre. A millilitre of water fills one 1-cm cube exactly. A litre fills a cube 10 cm on each side: 10 layers of 100 cubes. Change litres and millilitres to cubic centimetres before you divide by a base area, and the answer comes out in centimetres.
This tank has a floor 10 cm by 10 cm and is 25 cm high. Choose an amount of water.
Tap an amount
- base area = 10 × 10 = 100 cm²
- 1 ℓ = 1000 ml = 1000 cm³
- depth = 1000 cm³ ÷ 100 cm² = 10 cm
A jug holds 1 ℓ 50 ml of water. What is the volume of the water in cubic centimetres?
Step 5
Water level in a tank, and pouring water between tanks
Poured water keeps its volume; only its depth changes. The water in a tank is a cuboid of its own: base area times depth. Use the water's depth, not the tank's height. After pouring, divide that same volume by the new tank's base area. A bigger floor gives a lower level, and a smaller floor a higher one.
Tank A is 30 cm long, 20 cm wide and 25 cm high, with water 12 cm deep. All of it is poured into empty Tank B, 40 cm long, 30 cm wide and 20 cm high. Find the new water level.
Tap Next step
A tank is 20 cm long and 10 cm wide. It holds 3 ℓ of water. How deep is the water?
Primary 6 volume questions, worked step by stepPicture the layers before you begin. Then open a hint, or show the working a line at a time.
A rectangular box is 15 cm long, 8 cm wide and 6 cm high. Find its volume.
- volume = length × breadth × height
- base area = 15 × 8 = 120 cm²
- volume = 120 × 6 = 720 cm³
A solid is made of two cuboids. The bottom cuboid is 12 cm long, 7 cm wide and 5 cm high. The cuboid on top is 6 cm long, 7 cm wide and 4 cm high. Find the volume of the solid.
- bottom cuboid = 12 × 7 × 5 = 420 cm³
- top cuboid = 6 × 7 × 4 = 168 cm³
- volume of the solid = 420 + 168 = 588 cm³
A cube has a volume of 729 cm³. (a) Find the length of one edge. (b) Find the area of one face.
- volume = edge × edge × edge
- edge = ∛729 = 9 cm, because 9 × 9 × 9 = 729
- area of one face = 9 × 9 = 81 cm²
A rectangular tank is 50 cm long and 30 cm wide. It contains 21 ℓ of water. Find the depth of the water.
- 1 ℓ = 1000 ml = 1000 cm³, so 21 ℓ = 21000 cm³
- base area = 50 × 30 = 1500 cm²
- depth = 21000 cm³ ÷ 1500 cm² = 14 cm
Tank A is 40 cm long, 25 cm wide and 30 cm high, and it is full of water. Water from Tank A is poured into an empty cube-shaped Tank B with an edge of 20 cm until Tank B is full. Find the height of the water left in Tank A.
- water in Tank B = 20 × 20 × 20 = 8000 cm³
- base area of Tank A = 40 × 25 = 1000 cm²
- drop in Tank A = 8000 cm³ ÷ 1000 cm² = 8 cm
- water left in Tank A = 30 − 8 = 22 cm
Step 6
Check yourself
Five quick volume questions. Each reply names the set of questions that practises it.
1. Find the volume of a cuboid 9 cm long, 4 cm wide and 5 cm high.
2. A cuboid has a volume of 840 cm³. Its base is 12 cm by 7 cm. Find its height.
3. A solid of unit cubes has 2 layers. Its top view is 7 squares, and the top layer has 3 cubes. How many unit cubes are in the solid?
4. How many cubic centimetres is 2.06 ℓ?
5. Tank X has a base area of 600 cm² and holds water 10 cm deep. All of it is poured into empty Tank Y, which has a base area of 400 cm². How deep is the water in Tank Y?
How to use this guide. Before your child taps a button, ask how many cubes cover the floor and how many layers there will be. Then let the drawing show whether that was right. Each step takes a few minutes.
As your child writes each line, ask for its unit out loud: cubic centimetres for a volume, square centimetres for a floor, centimetres for a side or a depth. When a line's unit matches what it should be, the method behind it is usually sound too.
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