GCSE Maths: Volume of cuboids, and units of volume and capacity (Higher)
Part of the GCSE Maths volume, surface area and 3d shapes chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Volume of cuboids, and units of volume and capacity
Volume is the amount of space inside a solid. We measure it by counting how many unit cubes fit inside. A cubic centimetre (cm3) is the volume of a cube whose edges are all 1 cm long. A cubic metre (m3) is a cube with 1 m edges, and a cubic millimetre (mm3) a tiny cube with 1 mm edges.
Look at the cuboid below, which is 4 cm long, 3 cm wide and 2 cm high. The bottom layer holds 4 × 3 = 12 cubes. There are 2 layers, so the whole cuboid holds 12 × 2 = 24 cubes: its volume is 24 cm3.
This always works, so the volume of a cuboid is length × width × height. A cube has all edges equal, so its volume is side × side × side. The three lengths must be in the same unit before you multiply.
Capacity. Liquids are measured in litres (l) and millilitres (ml). The capacity of a container is how much it can hold. The links to volume are worth learning:
| Volume | Capacity |
|---|---|
| 1 cm3 | 1 ml |
| 1000 cm3 | 1 litre (1000 ml) |
| 1 m3 = 1,000,000 cm3 | 1000 litres |
| 1 cm3 | 1000 mm3 |
Why is 1 m3 equal to 1,000,000 cm3? Because 1 m = 100 cm, so a cube of side 1 m has volume 100 × 100 × 100 = 1,000,000 cm3. In the same way 1 cm = 10 mm, so 1 cm3 = 10 × 10 × 10 = 1000 mm3. Volume units are not like length units: you cube the conversion factor.
Key ideas
- Volume of a cuboid = length × width × height. Volume of a cube = side3.
- Volume is measured in cubic units: mm3, cm3, m3.
- 1 ml = 1 cm3. 1 litre = 1000 ml = 1000 cm3. 1 m3 = 1000 litres = 1,000,000 cm3.
- To find a missing length, divide the volume by the other two lengths.
- Put all lengths in the same unit before you multiply.
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in cm, so the units match.V = 8 × 5 × 4
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.8 × 5 = 40
- Multiply by the height. This counts all the layers.40 × 4 = 160
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 160 cm3
Check. Multiply in a different order: 5 × 4 = 20, then 20 × 8 = 160. ✓
Watch out. Volume is in cm3, not cm or cm2. Do not add the lengths.
Method. Use Volume = length × width × height with the unknown length as a letter, then divide to find it.
- Write the volume formula with the numbers you know. Volume = length × width × height. We call the missing length h.240 = 8 × 5 × h
- Multiply the two known lengths. Join the known numbers into one number.8 × 5 = 40, so 240 = 40 × h
- Divide to undo the multiplication. Dividing is the inverse of multiplying.h = 240 ÷ 40 = 6
- Write the unit. This is a length, so it is in cm (not cm3).h = 6 cm
Check. 8 × 5 × 6 = 240. ✓
Watch out. Divide the volume by the two known lengths, not by just one of them.
Method. Find the volume in cm3, then divide by 1000 to change cm3 into litres.
- Work out the volume of the cuboid. Volume = length × width × height, all in cm.80 × 50 = 4000
4000 × 40 = 160,000 cm3 - Change cm3 to litres. 1 litre = 1000 cm3, so divide by 1000.160,000 ÷ 1000 = 160
- Write the answer. Capacity = 160 litres
Check. 160 litres × 1000 = 160,000 cm3. ✓
Watch out. 1 litre is 1000 cm3. Do not divide by 100.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Change m3 into cm3. 1 m = 100 cm, so 1 m3 = 100 × 100 × 100 = 1,000,000 cm3.2.5 m3 = 2.5 × 1,000,000 = 2,500,000 cm3
- Change cm3 into litres. 1 litre = 1000 ml = 1000 cm3. To go to the bigger unit, divide.2,500,000 cm3 = 2,500,000 ÷ 1000 = 2500 litres
- Write the answer. Check that the unit matches what the question asked for.2.5 m3 = 2500 litres
Check. Go back the other way: 2500 litres gives 2.5 m3. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Method. A cube of side a has volume a × a × a. To find the side, find the number that multiplies by itself three times to give the volume (the cube root).
- Write the volume as a cube. We are looking for a number a with a × a × a = the volume.a × a × a = 343
- Try whole numbers. Test cubes you know: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.7 × 7 × 7 = 49 × 7 = 343
- State the side length. The side is the cube root of the volume.a = 7 cm
Check. 7 × 7 × 7 = 343. ✓
Watch out. The cube root is not the volume divided by 3.
Method. Write the new volume using the doubled lengths, then compare it with the old volume.
- Write the original volume. Volume = length × width × height.V = l × w × h
- Double each edge. The new edges are 2l, 2w and 2h.New volume = 2l × 2w × 2h
- Collect the numbers. Multiplication can be done in any order, so group the 2s.= 2 × 2 × 2 × l × w × h = 8lwh
- Compare. lwh is the original volume.New volume = 8 × V. So the volume is multiplied by 8. ✓
Check. Try l = w = h = 1: volume 1. Doubled: 2 × 2 × 2 = 8. ✓
Watch out. Doubling every length multiplies the volume by 23 = 8, not by 2. (See Chapter 21: similar solids.)
Watch out
Volume is in cubic units (cm3), so do not write cm or cm2. Do not add the lengths: multiply them. And do not change m3 to cm3 by multiplying by 100: you must multiply by 100 × 100 × 100 = 1,000,000.Exercise 19D Volume of cuboids and units of volume
Non-calculatorMethod. Count the cubes in one layer: they form a rectangle 4 by 3.
- Find the sides of the layer. The layer is 4 cubes long and 3 cubes wide.4 by 3
- Multiply. Rows × cubes in each row.4 × 3 = 12
Check. Count the cubes in 3 rows of 4: 4 + 4 + 4 = 12. ✓
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in cm, so the units match.V = 4 × 3 × 2
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.4 × 3 = 12
- Multiply by the height. This counts all the layers.12 × 2 = 24
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 24 cm3
Check. Multiply in a different order: 3 × 2 = 6, then 6 × 4 = 24. ✓
Watch out. Volume is in cm3, not cm or cm2. Do not add the lengths.
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in cm, so the units match.V = 5 × 4 × 3
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.5 × 4 = 20
- Multiply by the height. This counts all the layers.20 × 3 = 60
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 60 cm3
Check. Multiply in a different order: 4 × 3 = 12, then 12 × 5 = 60. ✓
Watch out. Volume is in cm3, not cm or cm2. Do not add the lengths.
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in cm, so the units match.V = 10 × 6 × 2
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.10 × 6 = 60
- Multiply by the height. This counts all the layers.60 × 2 = 120
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 120 cm3
Check. Multiply in a different order: 6 × 2 = 12, then 12 × 10 = 120. ✓
Watch out. Volume is in cm3, not cm or cm2. Do not add the lengths.
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in cm, so the units match.V = 2.5 × 4 × 6
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.2.5 × 4 = 10
- Multiply by the height. This counts all the layers.10 × 6 = 60
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 60 cm3
Check. Multiply in a different order: 4 × 6 = 24, then 24 × 2.5 = 60. ✓
Watch out. Volume is in cm3, not cm or cm2. Do not add the lengths.
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in m, so the units match.V = 3 × 2 × 1.5
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.3 × 2 = 6
- Multiply by the height. This counts all the layers.6 × 1.5 = 9
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 9 m3
Check. Multiply in a different order: 2 × 1.5 = 3, then 3 × 3 = 9. ✓
Watch out. Volume is in m3, not m or m2. Do not add the lengths.
Method. A cube has three equal lengths, so Volume = side × side × side.
- Write down the formula. Length, width and height of a cube are all the same size.V = side × side × side
- Substitute the side length. V = 6 × 6 × 6
- Multiply two of them first. Do it in two small steps.6 × 6 = 36
- Multiply by the last one. 36 × 6 = 216
- Write the unit. Cubic units.V = 216 cm3
Check. 63 on a calculator gives 216. ✓
Watch out. 63 means 6 × 6 × 6, not 6 × 3.
Method. A cube has three equal lengths, so Volume = side × side × side.
- Write down the formula. Length, width and height of a cube are all the same size.V = side × side × side
- Substitute the side length. V = 9 × 9 × 9
- Multiply two of them first. Do it in two small steps.9 × 9 = 81
- Multiply by the last one. 81 × 9 = 729
- Write the unit. Cubic units.V = 729 cm3
Check. 93 on a calculator gives 729. ✓
Watch out. 93 means 9 × 9 × 9, not 9 × 3.
Method. A cube has three equal lengths, so Volume = side × side × side.
- Write down the formula. Length, width and height of a cube are all the same size.V = side × side × side
- Substitute the side length. V = 20 × 20 × 20
- Multiply two of them first. Do it in two small steps.20 × 20 = 400
- Multiply by the last one. 400 × 20 = 8000
- Write the unit. Cubic units.V = 8000 mm3
Check. 203 on a calculator gives 8000. ✓
Watch out. 203 means 20 × 20 × 20, not 20 × 3.
Method. Use Volume = length × width × height with the unknown length as a letter, then divide to find it.
- Write the volume formula with the numbers you know. Volume = length × width × height. We call the missing length h.240 = 8 × 5 × h
- Multiply the two known lengths. Join the known numbers into one number.8 × 5 = 40, so 240 = 40 × h
- Divide to undo the multiplication. Dividing is the inverse of multiplying.h = 240 ÷ 40 = 6
- Write the unit. This is a length, so it is in cm (not cm3).h = 6 cm
Check. 8 × 5 × 6 = 240. ✓
Watch out. Divide the volume by the two known lengths, not by just one of them.
Method. Use Volume = length × width × height with the unknown length as a letter, then divide to find it.
- Write the volume formula with the numbers you know. Volume = length × width × height. We call the missing length w.180 = 6 × 5 × w
- Multiply the two known lengths. Join the known numbers into one number.6 × 5 = 30, so 180 = 30 × w
- Divide to undo the multiplication. Dividing is the inverse of multiplying.w = 180 ÷ 30 = 6
- Write the unit. This is a length, so it is in cm (not cm3).w = 6 cm
Check. 6 × 5 × 6 = 180. ✓
Watch out. Divide the volume by the two known lengths, not by just one of them.
Method. Use Volume = length × width × height with the unknown length as a letter, then divide to find it.
- Write the volume formula with the numbers you know. Volume = length × width × height. We call the missing length l.96 = 4 × 3 × l
- Multiply the two known lengths. Join the known numbers into one number.4 × 3 = 12, so 96 = 12 × l
- Divide to undo the multiplication. Dividing is the inverse of multiplying.l = 96 ÷ 12 = 8
- Write the unit. This is a length, so it is in cm (not cm3).l = 8 cm
Check. 4 × 3 × 8 = 96. ✓
Watch out. Divide the volume by the two known lengths, not by just one of them.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Change litres into cm3. 1 litre = 1000 ml = 1000 cm3.3 litres = 3 × 1000 = 3000 cm3
- Change cm3 into ml. 1 millilitre (ml) is the same amount as 1 cm3.3000 cm3 = 3000 ml
- Write the answer. Check that the unit matches what the question asked for.3 litres = 3000 ml
Check. Go back the other way: 3000 ml gives 3 litres. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Change ml into cm3. 1 millilitre (ml) is the same amount as 1 cm3.4500 ml = 4500 cm3
- Change cm3 into litres. 1 litre = 1000 ml = 1000 cm3. To go to the bigger unit, divide.4500 cm3 = 4500 ÷ 1000 = 4.5 litres
- Write the answer. Check that the unit matches what the question asked for.4500 ml = 4.5 litres
Check. Go back the other way: 4.5 litres gives 4500 ml. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Decide which conversion fact we need. Every volume unit can be linked to cm3.1 litre = 1000 ml = 1000 cm3
- Change cm3 into litres. 1 litre = 1000 ml = 1000 cm3. To go to the bigger unit, divide.2000 cm3 = 2000 ÷ 1000 = 2 litres
- Write the answer. Check that the unit matches what the question asked for.2000 cm3 = 2 litres
Check. Go back the other way: 2 litres gives 2000 cm3. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Change m3 into cm3. 1 m = 100 cm, so 1 m3 = 100 × 100 × 100 = 1,000,000 cm3.0.5 m3 = 0.5 × 1,000,000 = 500,000 cm3
- Change cm3 into litres. 1 litre = 1000 ml = 1000 cm3. To go to the bigger unit, divide.500,000 cm3 = 500,000 ÷ 1000 = 500 litres
- Write the answer. Check that the unit matches what the question asked for.0.5 m3 = 500 litres
Check. Go back the other way: 500 litres gives 0.5 m3. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Decide which conversion fact we need. Every volume unit can be linked to cm3.1 m = 100 cm, so 1 m3 = 100 × 100 × 100 = 1,000,000 cm3
- Change m3 into cm3. 1 m = 100 cm, so 1 m3 = 100 × 100 × 100 = 1,000,000 cm3.5 m3 = 5 × 1,000,000 = 5,000,000 cm3
- Write the answer. Check that the unit matches what the question asked for.5 m3 = 5,000,000 cm3
Check. Go back the other way: 5,000,000 cm3 gives 5 m3. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Decide which conversion fact we need. Every volume unit can be linked to cm3.1 cm = 10 mm, so 1 cm3 = 10 × 10 × 10 = 1000 mm3
- Change mm3 into cm3. 1 cm = 10 mm, so 1 cm3 = 10 × 10 × 10 = 1000 mm3.7000 mm3 = 7000 ÷ 1000 = 7 cm3
- Write the answer. Check that the unit matches what the question asked for.7000 mm3 = 7 cm3
Check. Go back the other way: 7 cm3 gives 7000 mm3. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Method. Find the volume in cm3, then divide by 1000 to change cm3 into litres.
- Work out the volume of the cuboid. Volume = length × width × height, all in cm.60 × 30 = 1800
1800 × 40 = 72,000 cm3 - Change cm3 to litres. 1 litre = 1000 cm3, so divide by 1000.72,000 ÷ 1000 = 72
- Write the answer. Capacity = 72 litres
Check. 72 litres × 1000 = 72,000 cm3. ✓
Watch out. 1 litre is 1000 cm3. Do not divide by 100.
Method. Find the capacity of the tank in litres, then divide by the rate of filling.
- Find the volume in cm3. Volume = length × width × height.80 × 50 = 4000, then 4000 × 40 = 160,000 cm3
- Change to litres. 1 litre = 1000 cm3, so divide by 1000.160,000 ÷ 1000 = 160 litres
- Divide by the rate. Each minute 8 litres go in, so count how many 8s make 160.160 ÷ 8 = 20 minutes
Check. In 20 minutes, 20 × 8 = 160 litres go in. ✓
Watch out. Change cm3 to litres before you use the rate in litres.
Method. Find how many cubes fit along each edge, then multiply. (Divide the volumes only if the cubes fit exactly.)
- Cubes along the length. Divide the length by the side of the cube.20 ÷ 5 = 4
- Cubes along the width. 15 ÷ 5 = 3
- Cubes up the height. 10 ÷ 5 = 2
- Multiply. This counts the cubes in one layer, then all the layers.4 × 3 × 2 = 24
Check. Volume of the box 20 × 15 × 10 = 3000; one cube is 5 × 5 × 5 = 125; 3000 ÷ 125 = 24. ✓
Watch out. Dividing the volumes works only when the cubes fit with no gaps.
Key words. Volume is the space inside a 3D shape. A cubic centimetre (cm3) is the volume of a cube with sides of 1 cm.
Method. Volume is the amount of space inside a solid. For a cuboid, multiply length × width × height.
- Write down the formula. A cuboid is built from layers of 1-unit cubes. One layer holds length × width cubes and the height tells us how many layers there are.Volume = length × width × height
- Substitute the lengths. All three lengths are in m, so the units match.V = 10 × 4 × 1.5
- Multiply the length and the width first. This is the area of the base: the number of cubes in one layer.10 × 4 = 40
- Multiply by the height. This counts all the layers.40 × 1.5 = 60
- Write the answer with its unit. Three lengths multiplied together give a cubic unit.V = 60 m3
Check. Multiply in a different order: 4 × 1.5 = 6, then 6 × 10 = 60. ✓
Watch out. Volume is in m3, not m or m2. Do not add the lengths.
Key words. Capacity is how much a container can hold, measured in litres (l) and millilitres (ml). Volume is the space a solid takes up.
Method. Change the volume to cm3 first, using the fact that links the unit to cm3, then change to the unit you want.
- Change m3 into cm3. 1 m = 100 cm, so 1 m3 = 100 × 100 × 100 = 1,000,000 cm3.60 m3 = 60 × 1,000,000 = 60,000,000 cm3
- Change cm3 into litres. 1 litre = 1000 ml = 1000 cm3. To go to the bigger unit, divide.60,000,000 cm3 = 60,000,000 ÷ 1000 = 60,000 litres
- Write the answer. Check that the unit matches what the question asked for.60 m3 = 60,000 litres
Check. Go back the other way: 60,000 litres gives 60 m3. ✓
Watch out. Volume units are not the same as length units: 1 m3 is 1,000,000 cm3, not 100 cm3.
Method. Work out both volumes, compare them, then find the difference.
- Volume of box A. length × width × height.30 × 20 = 600, then 600 × 10 = 6000 cm3
- Volume of box B. 25 × 25 = 625, then 625 × 10 = 6250 cm3
- Compare and subtract. Box B is bigger. Subtract the smaller from the larger.6250 − 6000 = 250
- Write the answer. Box B is larger, by 250 cm3.
Check. B is 625 × 10, A is 600 × 10, so B is 25 × 10 = 250 bigger. ✓
Method. Check which operation the volume formula uses, then redo the calculation.
- Spot the mistake. Volume = length × width × height. Tom added the lengths, which would give something like the total of three edges, not a volume.Tom added instead of multiplying.
- Do it correctly. Multiply the first two, then the third.6 × 4 = 24, then 24 × 3 = 72
- Write the answer with its unit. Volume = 72 cm3
Check. 3 layers of 24 cubes: 3 × 24 = 72. ✓
Watch out. Volume needs multiplication, not addition.
Method. Find whole numbers that multiply to give 36. Start with a factor pair of 36 and split one factor again.
- List the factors of 36. The edges must be factors of 36.1, 2, 3, 4, 6, 9, 12, 18, 36
- Choose three that multiply to 36. Try combinations and check the product.36 × 1 × 1 = 36
18 × 2 × 1 = 36
12 × 3 × 1 = 36
9 × 4 × 1 = 36
9 × 2 × 2 = 36
6 × 6 × 1 = 36
6 × 3 × 2 = 36
4 × 3 × 3 = 36 - Write three of them. Any three of these sets are correct.36 × 1 × 1, 18 × 2 × 1, 12 × 3 × 1
Check. Each product is 36, and each set uses whole numbers. ✓
Method. A cubic metre is a cube. Work out how many 1 cm cubes it holds.
- Think of a cube of side 1 m. 1 m = 100 cm, so the cube is 100 cm long, 100 cm wide and 100 cm high.100 cm × 100 cm × 100 cm
- Work out its volume in cm3. Volume = length × width × height.100 × 100 = 10,000, then 10,000 × 100 = 1,000,000
- Compare with Jo. Jo multiplied the conversion factor once instead of three times.1 m3 = 1,000,000 cm3, not 100 cm3.
Check. 1 litre = 1000 cm3 and 1 m3 = 1000 litres, so 1000 × 1000 = 1,000,000. ✓
Method. Let the side of the base be x. Then the height is 3x. Write the volume as an equation and solve it.
- Write the dimensions using x. The base is square so length and width are both x. The height is 3x.x, x and 3x
- Write the volume equation. Volume = length × width × height.x × x × 3x = 3x3 = 192
- Divide by 3. x3 = 64
- Cube root. 4 × 4 × 4 = 64.x = 4
- Find the height. Height = 3x.3 × 4 = 12. The cuboid is 4 cm by 4 cm by 12 cm.
Check. 4 × 4 × 12 = 192. ✓
Method. If every edge is multiplied by 3, the volume is multiplied by 3 × 3 × 3.
- Find the volume scale factor. The three lengths length, width and height are each multiplied by 3.3 × 3 × 3 = 27
- Multiply the volume. 24 × 27 = 648
- Write the unit. 648 cm3
Check. Try edges 4, 3, 2: volume 24. New edges 12, 9, 6: 12 × 9 × 6 = 648. ✓
Watch out. Multiply by the scale factor cubed, not just by 3.