GCSE Maths: Area and volume units (Foundation)
Part of the GCSE Maths units and compound measures chapter (Foundation). Chapter overview · Higher version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Area and volume units
Length is measured in a single direction, so its units are cm, m, km. Area measures a flat surface, so its units are square units: cm² means “squares with sides of 1 cm”. Volume measures the space inside a 3D shape, so its units are cubic units: cm³ means “cubes with edges of 1 cm”. Because of this, the conversion factors for area and volume are not the same as for length.
Why the factor is squared
Look at a square with sides of 1 m. Each side is also 100 cm. The square is 100 cm long and 100 cm wide, so it holds 100 × 100 = 10 000 squares of 1 cm². So 1 m² = 10 000 cm², not 100 cm². The area factor is the length factor squared.
Why the factor is cubed
A cube with edges of 1 m has edges of 100 cm. It holds 100 × 100 × 100 = 1 000 000 cubes of 1 cm³. So 1 m³ = 1 000 000 cm³. The volume factor is the length factor cubed.
Facts to know
| Length | Area | Volume |
|---|---|---|
| 1 cm = 10 mm | 1 cm² = 100 mm² | 1 cm³ = 1000 mm³ |
| 1 m = 100 cm | 1 m² = 10 000 cm² | 1 m³ = 1 000 000 cm³ |
| 1 km = 1000 m | 1 km² = 1 000 000 m² | 1 km³ = 1 000 000 000 m³ |
Volume and capacity are two ways of measuring the same amount: 1 ml = 1 cm³, 1 litre = 1000 cm³ and 1 m³ = 1000 litres. So a fish tank that has volume 30 000 cm³ holds 30 litres.
The method
(1) Write the length fact. (2) Square it for area, cube it for volume. (3) Multiply if you are changing to a smaller unit, divide if you are changing to a bigger unit. You can also change all the lengths to the new unit before you work out the area or volume, which avoids the squared factor altogether.
Key ideas
- Area factor = (length factor)². Volume factor = (length factor)³.
- 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³.
- 1 ml = 1 cm³, 1 litre = 1000 cm³, 1 m³ = 1000 litres.
- Smaller unit: multiply. Bigger unit: divide.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.3.5 × 10,000 = 35,000 cm²
Check. Convert back: 35,000 cm² ÷ 10,000 = 3.5 m². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.45,000 ÷ 10,000 = 4.5 m²
Check. Convert back: 4.5 m² × 10,000 = 45,000 cm². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm³ fit in 1 m³. A cube of side 1 m has side 100 cm. Its volume is the length cubed. The number of small cubes is length × length × length.1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm³ is bigger.0.004 × 1,000,000 = 4000 cm³
Check. Convert back: 4000 cm³ ÷ 1,000,000 = 0.004 m³. ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 1,000,000 cm³.
Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.
- Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.1 litre = 1000 cm³ (and 1 ml = 1 cm³)
- Decide: multiply or divide? We are changing to the bigger unit, so we need fewer of them: divide by 1000.36,000 ÷ 1000
- Calculate. 36,000 ÷ 1000 = 36 litres
Check. Convert back: 36 litres × 1000 = 36,000 cm³. ✓
Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.
Method. Write all three lengths in the same unit first (centimetres), find the volume, then change cm³ to litres.
- Change 1.5 m to cm. Metres to centimetres: multiply by 100.1.5 × 100 = 150 cm
- Find the volume. Volume of a cuboid = length × width × height.150 × 80 × 50 = 600000 cm³
- Change cm³ to litres. 1 litre = 1000 cm³, and cm³ to litres means divide by 1000.600000 ÷ 1000 = 600 litres
Check. In metres: 1.5 × 0.8 × 0.5 = 0.6 m³ and 0.6 × 1000 = 600 litres. ✓
Watch out. Do not multiply 1.5 × 80 × 50 with mixed units. Always match the units before you multiply.
Watch out
1 m = 100 cm, but 1 m² is not 100 cm², and 1 m³ is not 100 cm³. Square or cube the factor. A quick check: 1 m² is a big square, so it must hold lots of tiny cm squares (10 000 of them).Exercise 16C Converting area and volume units
Non-calculatorKey words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.1 cm² = 10 mm × 10 mm = 100 mm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm² is bigger.1 × 100 = 100 mm²
Check. Convert back: 100 mm² ÷ 100 = 1 cm². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.2 × 10,000 = 20,000 cm²
Check. Convert back: 20,000 cm² ÷ 10,000 = 2 m². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.0.5 × 10,000 = 5000 cm²
Check. Convert back: 5000 cm² ÷ 10,000 = 0.5 m². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.1 cm² = 10 mm × 10 mm = 100 mm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm² is bigger.3 × 100 = 300 mm²
Check. Convert back: 300 mm² ÷ 100 = 3 cm². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.1 cm² = 10 mm × 10 mm = 100 mm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm² is bigger.1.2 × 100 = 120 mm²
Check. Convert back: 120 mm² ÷ 100 = 1.2 cm². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.50,000 ÷ 10,000 = 5 m²
Check. Convert back: 5 m² × 10,000 = 50,000 cm². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.25,000 ÷ 10,000 = 2.5 m²
Check. Convert back: 2.5 m² × 10,000 = 25,000 cm². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.1 cm² = 10 mm × 10 mm = 100 mm²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of cm² is smaller.700 ÷ 100 = 7 cm²
Check. Convert back: 7 cm² × 100 = 700 mm². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm² fit in 1 cm². A square of side 1 cm has side 10 mm. Its area is the length squared. The number of small squares is length × length.1 cm² = 10 mm × 10 mm = 100 mm²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of cm² is smaller.450 ÷ 100 = 4.5 cm²
Check. Convert back: 4.5 cm² × 100 = 450 mm². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 km = 1000 m
- Find how many m² fit in 1 km². A square of side 1 km has side 1000 m. Its area is the length squared. The number of small squares is length × length.1 km² = 1000 m × 1000 m = 1,000,000 m²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of m² is bigger.2 × 1,000,000 = 2,000,000 m²
Check. Convert back: 2,000,000 m² ÷ 1,000,000 = 2 km². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 km = 1000 m
- Find how many m² fit in 1 km². A square of side 1 km has side 1000 m. Its area is the length squared. The number of small squares is length × length.1 km² = 1000 m × 1000 m = 1,000,000 m²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of km² is smaller.3,500,000 ÷ 1,000,000 = 3.5 km²
Check. Convert back: 3.5 km² × 1,000,000 = 3,500,000 m². ✓
Watch out. Use the square of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm² is bigger.0.04 × 10,000 = 400 cm²
Check. Convert back: 400 cm² ÷ 10,000 = 0.04 m². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change area units, square (or cube) the length factor. The area factor is the length factor squared.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm² fit in 1 m². A square of side 1 m has side 100 cm. Its area is the length squared. The number of small squares is length × length.1 m² = 100 cm × 100 cm = 10,000 cm²
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of m² is smaller.62,000 ÷ 10,000 = 6.2 m²
Check. Convert back: 6.2 m² × 10,000 = 62,000 cm². ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 10,000 cm².
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm³ fit in 1 m³. A cube of side 1 m has side 100 cm. Its volume is the length cubed. The number of small cubes is length × length × length.1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of cm³ is bigger.3 × 1,000,000 = 3,000,000 cm³
Check. Convert back: 3,000,000 cm³ ÷ 1,000,000 = 3 m³. ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 1,000,000 cm³.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm³ fit in 1 cm³. A cube of side 1 cm has side 10 mm. Its volume is the length cubed. The number of small cubes is length × length × length.1 cm³ = 10 mm × 10 mm × 10 mm = 1000 mm³
- Multiply by the area/volume factor. We are changing to the smaller unit, so the number of mm³ is bigger.2.5 × 1000 = 2500 mm³
Check. Convert back: 2500 mm³ ÷ 1000 = 2.5 cm³. ✓
Watch out. Use the cube of the length factor, not the length factor itself.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 m = 100 cm
- Find how many cm³ fit in 1 m³. A cube of side 1 m has side 100 cm. Its volume is the length cubed. The number of small cubes is length × length × length.1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of m³ is smaller.4,500,000 ÷ 1,000,000 = 4.5 m³
Check. Convert back: 4.5 m³ × 1,000,000 = 4,500,000 cm³. ✓
Watch out. Do not use the length factor on its own. 1 m = 100 cm but 1 m² is not 100 cm²; it is 1,000,000 cm³.
Key words. Area is the amount of flat surface, measured in square units such as cm². Volume is the space inside a 3D shape, measured in cubic units such as cm³.
Method. To change volume units, square (or cube) the length factor. The volume factor is the length factor cubed.
- Write the length fact for the two units. Area and volume units are built from lengths, so start with the length fact.1 cm = 10 mm
- Find how many mm³ fit in 1 cm³. A cube of side 1 cm has side 10 mm. Its volume is the length cubed. The number of small cubes is length × length × length.1 cm³ = 10 mm × 10 mm × 10 mm = 1000 mm³
- Divide by the area/volume factor. We are changing to the bigger unit, so the number of cm³ is smaller.6000 ÷ 1000 = 6 cm³
Check. Convert back: 6 cm³ × 1000 = 6000 mm³. ✓
Watch out. Use the cube of the length factor, not the length factor itself.
Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.
- Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.1 litre = 1000 cm³ (and 1 ml = 1 cm³)
- Decide: multiply or divide? We are changing to the bigger unit, so we need fewer of them: divide by 1000.4500 ÷ 1000
- Calculate. 4500 ÷ 1000 = 4.5 litres
Check. Convert back: 4.5 litres × 1000 = 4500 cm³. ✓
Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.
Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.
- Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.1 litre = 1000 cm³ (and 1 ml = 1 cm³)
- Decide: multiply or divide? There are 1000 small units in every big one, so changing to the smaller unit gives a bigger number: multiply.3 × 1000
- Calculate. 3 × 1000 = 3000 cm³
Check. Convert back: 3000 cm³ ÷ 1000 = 3 litres. ✓
Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.
Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.
- Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.1 m³ = 1000 litres (and 1 ml = 1 cm³)
- Decide: multiply or divide? There are 1000 small units in every big one, so changing to the smaller unit gives a bigger number: multiply.2 × 1000
- Calculate. 2 × 1000 = 2000 litres
Check. Convert back: 2000 litres ÷ 1000 = 2 m³. ✓
Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.
Method. Volume and capacity are linked by a fact you must know. Use it to multiply or divide.
- Write the link between the units. Capacity (litres, ml) measures liquids; volume (cm³, m³) measures space. They are two ways to measure the same amount.1 m³ = 1000 litres (and 1 ml = 1 cm³)
- Decide: multiply or divide? We are changing to the bigger unit, so we need fewer of them: divide by 1000.750 ÷ 1000
- Calculate. 750 ÷ 1000 = 0.75 m³
Check. Convert back: 0.75 m³ × 1000 = 750 litres. ✓
Watch out. 1 litre is 1000 cm³ (not 100 and not 10 000). Think of a 10 cm cube: 10 × 10 × 10 = 1000 cm³ holds exactly 1 litre.
Method. Find the volume in cm³ first, then change to mm³.
- Volume in cm³. Volume of a cuboid = length × width × height.2 × 3 × 4 = 24 cm³
- Find the cm³ to mm³ factor. 1 cm = 10 mm, so 1 cm³ = 10 × 10 × 10 mm³.1 cm³ = 1000 mm³
- Multiply. mm³ is the smaller unit, so the number gets bigger.24 × 1000 = 24000 mm³
Check. In mm: 20 × 30 × 40 = 24 000 mm³. ✓
Method. Find the area in m², then change to cm² with the factor 10 000.
- Find the area. Area of a rectangle = length × width.4 × 2.5 = 10 m²
- Use 1 m² = 10 000 cm². Changing to a smaller unit: multiply.10 × 10 000 = 100000 cm²
- Write the answer. 100 000 cm²
Check. In cm: 400 × 250 = 100 000 cm². ✓
Watch out. Do not multiply by 100 only. The area factor is 10 000.
Method. Find the area of the floor and of one tile in the same unit, then divide.
- Change the floor to cm. 3 m = 300 cm and 2 m = 200 cm.300 cm by 200 cm
- Area of the floor and of a tile. Area = length × width.Floor: 300 × 200 = 60000 cm²
Tile: 20 × 20 = 400 cm² - Divide. How many tiles fit in the floor area?60000 ÷ 400 = 150
Check. Along the length: 300 ÷ 20 = 15 tiles. Across: 200 ÷ 20 = 10 tiles. 15 × 10 = 150. ✓
Method. Draw (or imagine) a square of side 1 m and count the small squares.
- Write the side lengths in cm. 1 m = 100 cm, so the square is 100 cm by 100 cm.100 cm by 100 cm
- Work out the area in cm². Area = length × width.100 × 100 = 10 000 cm²
- Explain. Kayla used the length factor for an area. Area has two dimensions, so the factor is squared.1 m² = 10 000 cm²
Check. A square metre is about the size of a small table top; 100 cm² would be about the size of a credit card. ✓
Method. Use one unit for all the lengths, find the volume, then change to litres.
- Change 1.5 m to cm. Metres to cm: multiply by 100.1.5 × 100 = 150 cm
- Find the volume. Length × width × height.150 × 80 × 50 = 600000 cm³
- Change to litres. 1 litre = 1000 cm³, so divide by 1000.600000 ÷ 1000 = 600 litres
Check. 0.6 m³ = 600 litres. ✓
Method. The water forms a cuboid, 60 cm by 30 cm by 30 cm deep. Find its volume and change to litres.
- Find the volume of the water. Use the depth of the water (30 cm), not the height of the tank.60 × 30 × 30 = 54000 cm³
- Change to litres. Divide by 1000.54000 ÷ 1000 = 54 litres
Check. If the tank were full: 60 × 30 × 40 = 72 000 cm³ = 72 litres. Our 54 is three quarters of 72. ✓
Watch out. Use the depth of the water, not the height of the tank.
Method. Change both areas to the same unit before comparing.
- Change 0.6 m² to cm². Multiply by 10 000.0.6 × 10 000 = 6000 cm²
- Compare. Both are now in cm².6000 cm² > 5500 cm²
- Write the answer. 0.6 m² is larger
Check. In m²: 5500 ÷ 10 000 = 0.55 m², and 0.55 < 0.6. ✓
Method. Find the volume in m³ and use 1 m³ = 1000 litres.
- Volume in m³. Length × width × depth.25 × 10 × 1.6 = 400 m³
- Change to litres. 1 m³ = 1000 litres, so multiply by 1000.400 × 1000 = 400,000 litres
Check. 400 m³ is 400 big cubes of 1 m, each holding 1000 litres. ✓
Method. Divide the volume by the rate, then change minutes to hours and minutes.
- Divide by the rate. Time = amount ÷ rate.400,000 ÷ 500 = 800 minutes
- Change to hours and minutes. 60 minutes = 1 hour.800 ÷ 60 = 13 remainder 20
13 hours 20 minutes
Check. 13 × 60 + 20 = 800 minutes. ✓