Year 5: Volume and capacity
Part of the Year 5 units, perimeter, area, volume and time chapter. Chapter overview · whole chapter on one page
Volume and capacity
The volume of a solid is the amount of space it takes up. We can find the volume by building the solid from 1 cm cubes. Each cube is 1 cm long, 1 cm wide and 1 cm high, so its volume is 1 cubic centimetre, written cm³.
The cuboid below is built in three layers. Each layer has 4 cubes along and 2 cubes across, so it has 8 cubes. Three layers of 8 cubes is 24 cubes, so the volume is 24 cm³.
Capacity is how much a container can hold. Liquids are measured in litres and millilitres. A millilitre is the same as a cubic centimetre: 1 ml = 1 cm³. There are 1,000 ml in 1 litre, so 1 litre = 1,000 cm³.
Key ideas
- Volume of a cuboid of cubes = cubes in one layer × number of layers.
- Volume is measured in cubic centimetres (cm³). Area is measured in square centimetres (cm²).
- 1 ml = 1 cm³. 1 litre = 1,000 ml = 1,000 cm³.
- To change litres to millilitres, multiply by 1,000. To change millilitres to litres, divide by 1,000.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.4 × 2 = 8 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.8 × 3 = 24 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.24 cm³
Check. 4 × 3 × 2 = 24 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 4 = 20 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.20 × 3 = 60 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.60 cm³
Check. 5 × 3 × 4 = 60 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. One millilitre is the same as one cubic centimetre, so the number does not change.
- Write the rule. A millilitre and a cubic centimetre are the same amount.1 ml = 1 cm³
- Use the same number. 750 millilitres is 750 of these small cubes.750 ml = 750 cm³
- Write the answer. 750 cm³
Check. A cube with sides of 10 cm holds 1000 cm³, which is 1000 ml. ✓
Watch out. Do not multiply by 10 or 100. The number stays the same.
Watch out
Do not count the cubes on one face only. Count the layers and the cubes in each layer, or you will miss the cubes inside. Also do not use cm² for volume: a volume is always in cubic units.Exercise 8E Volume and capacity
Non-calculatorKey words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 2 = 10 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.10 × 3 = 30 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.30 cm³
Check. 5 × 3 × 2 = 30 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.2 × 3 = 6 cubes in one layer
- Count the layers. The layers are stacked on top of each other.4 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.6 × 4 = 24 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.24 cm³
Check. 2 × 4 × 3 = 24 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 2 = 10 cubes in one layer
- Count the layers. The layers are stacked on top of each other.2 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.10 × 2 = 20 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.20 cm³
Check. 5 × 2 × 2 = 20 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.3 × 3 = 9 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.9 × 3 = 27 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.27 cm³
Check. 3 × 3 × 3 = 27 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.6 × 2 = 12 cubes in one layer
- Count the layers. The layers are stacked on top of each other.1 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.12 × 1 = 12 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.12 cm³
Check. 6 × 1 × 2 = 12 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.4 × 4 = 16 cubes in one layer
- Count the layers. The layers are stacked on top of each other.4 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.16 × 4 = 64 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.64 cm³
Check. 4 × 4 × 4 = 64 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.10 × 5 = 50 cubes in one layer
- Count the layers. The layers are stacked on top of each other.2 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.50 × 2 = 100 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.100 cm³
Check. 10 × 2 × 5 = 100 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. A cube with sides of 10 cm is built from 1 cm cubes, so its volume is 1000 cm³.
- Find the volume of the cube. Each of the 10 layers has 10 × 10 cubes.10 × 10 × 10 = 1000 cm³
- Use the rule 1 ml = 1 cm³. A millilitre is the same as a cubic centimetre, so the number is the same.1000 cm³ = 1000 ml
- Write the answer. There are 1,000 ml in 1 litre, so this is exactly 1 litre.1000 ml (1 litre)
Check. 1000 ml ÷ 1000 = 1 litre. ✓
Watch out. The number does not change when you change cm³ to ml.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. One millilitre is the same as one cubic centimetre, so the number does not change.
- Write the rule. A millilitre and a cubic centimetre are the same amount.1 ml = 1 cm³
- Use the same number. 750 millilitres is 750 of these small cubes.750 ml = 750 cm³
- Write the answer. 750 cm³
Check. A cube with sides of 10 cm holds 1000 cm³, which is 1000 ml. ✓
Watch out. Do not multiply by 10 or 100. The number stays the same.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 1,000 = 2,500
- Write the answer with the new unit. 2,500 ml
Check. 2,500 ÷ 1,000 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. One litre is 1,000 ml, and each millilitre is 1 cm³.
- Write what one litre is in millilitres. There are 1,000 ml in 1 litre.1 litre = 1,000 ml
- Change the millilitres to cubic centimetres. One millilitre is 1 cm³, so the number is the same.1,000 ml = 1,000 cm³
- Write the answer. 1,000 cm³
Check. 1,000 cm³ is a cube with sides of 10 cm. ✓
Watch out. 1 litre is 1,000 cm³, not 100 cm³.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find out how much is missing from 1 litre. The jug has 600 ml, so take it away from 1000 ml.
- Read the amount in the jug. The jug has 600 ml of water.600 ml
- Take it away from 1 litre. One litre is 1,000 ml, so the jug needs 1,000 ml when it is full.1,000 − 600 = 400 ml
- Write the answer. 400 ml
Check. 600 ml + 400 ml = 1,000 ml, which is 1 litre. ✓
Watch out. Take the amount in the jug away from 1,000 ml, not from 600 ml.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the volume of each box, then compare.
- Find the volume of the first box. Multiply the three sides.4 × 3 × 2 = 24 cm³
- Find the volume of the second box. Multiply the three sides.6 × 4 × 1 = 24 cm³
- Write the answer. The volumes are equal.Yes. Both boxes have a volume of 24 cm³.
Check. Different shapes can have the same volume. ✓
Watch out. A box that looks bigger does not always hold more. Multiply the three sides.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. The base area is length × width. The volume divided by the base area is the height.
- Find the area of the base. Multiply the length by the width.6 × 2 = 12 cm²
- Find the height. The volume is the base multiplied by the height, so divide the volume by the base.24 ÷ 12 = 2
- Write the answer. 2 cm
Check. 12 × 2 = 24 cm³. ✓
Watch out. Divide the volume by the base, not by the length alone.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.4 × 3 = 12 cubes in one layer
- Count the layers. The layers are stacked on top of each other.5 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.12 × 5 = 60 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.60 cm³
Check. 4 × 5 × 3 = 60 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the volume in cm³, then change it to litres.
- Find the volume in cm³. Each layer of the base has 40 × 25 cubes, so the base area is 1,000 cm².40 × 25 = 1000 cm²
- Multiply by the height. The tank is 30 cm high, so there are 30 layers.1000 × 30 = 30,000 cm³
- Change cm³ to litres. 1 litre = 1,000 cm³, so divide by 1,000.30,000 ÷ 1,000 = 30 litres
- Write the answer. 30 litres
Check. 30 litres × 1000 = 30,000 cm³. ✓
Watch out. Check the unit: 1 litre is 1,000 cm³, not 100 cm³.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the side length of a cube with volume 27 cm³.
- Write the volume as a cube. A cube has the same length, width and height.side × side × side = 27
- Find the number that works. Try 1, 2, 3 ... until the product is 27. 1 × 1 × 1 = 1 and 2 × 2 × 2 = 8.3 × 3 × 3 = 27
- Write the answer. 3 cm
Check. 3 × 9 = 27 cm³. ✓
Watch out. A cube has the same length on all three sides. Multiply the side by itself three times.