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Mensuration - Converting Units of Area and Volume

Grade 8IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Understanding the Relationship: Area and Volume conversions are not linear. If the scale factor for length is k, the scale factor for area is k² and for volume is k³.

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Larger to Smaller Units: When converting from a larger unit (e.g., m²) to a smaller unit (e.g., cm²), multiply by the conversion factor.

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Smaller to Larger Units: When converting from a smaller unit (e.g., mm³) to a larger unit (e.g., cm³), divide by the conversion factor.

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Capacity vs Volume: Liquid capacity is often measured in Litres (L) and Millilitres (ml), where 1cm3=1ml1 cm^3 = 1 ml and 1000cm3=1L1000 cm^3 = 1 L.

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Hectares: A specific metric unit for land area where 1 hectare=10,000m21 \text{ hectare} = 10,000 m^2.

📐Formulae

1 cm2=102 mm2=100 mm21 \text{ cm}^2 = 10^2 \text{ mm}^2 = 100 \text{ mm}^2

1 m2=1002 cm2=10,000 cm21 \text{ m}^2 = 100^2 \text{ cm}^2 = 10,000 \text{ cm}^2

1 km2=1,0002 m2=1,000,000 m21 \text{ km}^2 = 1,000^2 \text{ m}^2 = 1,000,000 \text{ m}^2

1 cm3=103 mm3=1,000 mm31 \text{ cm}^3 = 10^3 \text{ mm}^3 = 1,000 \text{ mm}^3

1 m3=1003 cm3=1,000,000 cm31 \text{ m}^3 = 100^3 \text{ cm}^3 = 1,000,000 \text{ cm}^3

1 Litre=1,000 cm3=1,000 ml1 \text{ Litre} = 1,000 \text{ cm}^3 = 1,000 \text{ ml}

1 m3=1,000 Litres1 \text{ m}^3 = 1,000 \text{ Litres}

💡Examples

Problem 1:

Convert 4.5 m24.5 \text{ m}^2 into  cm2\text{ cm}^2.

Solution:

4.5×10,000=45,000 cm24.5 \times 10,000 = 45,000 \text{ cm}^2

Explanation:

Since 1 m=100 cm1 \text{ m} = 100 \text{ cm}, the area conversion factor is 1002=10,000100^2 = 10,000. To go from a larger unit (m) to a smaller unit (cm), we multiply.

Problem 2:

A water tank holds 2.8 m32.8 \text{ m}^3 of water. Calculate its capacity in Litres.

Solution:

2.8×1,000=2,800 Litres2.8 \times 1,000 = 2,800 \text{ Litres}

Explanation:

We know that 1 m31 \text{ m}^3 contains 1,000,000 cm31,000,000 \text{ cm}^3 and 1,000 cm3=1 Litre1,000 \text{ cm}^3 = 1 \text{ Litre}. Therefore, 1 m3=1,000 Litres1 \text{ m}^3 = 1,000 \text{ Litres}. Multiplying 2.82.8 by 1,0001,000 gives the capacity.

Problem 3:

Convert 7,500 mm37,500 \text{ mm}^3 into  cm3\text{ cm}^3.

Solution:

7,500÷1,000=7.5 cm37,500 \div 1,000 = 7.5 \text{ cm}^3

Explanation:

Since 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}, the volume conversion factor is 103=1,00010^3 = 1,000. To go from a smaller unit (mm) to a larger unit (cm), we divide.

Problem 4:

A field has an area of 0.05 km20.05 \text{ km}^2. Find its area in hectares.

Solution:

0.05 km2=50,000 m20.05 \text{ km}^2 = 50,000 \text{ m}^2. Since 10,000 m2=1 hectare10,000 \text{ m}^2 = 1 \text{ hectare}, then 50,000÷10,000=5 hectares50,000 \div 10,000 = 5 \text{ hectares}.

Explanation:

First, convert  km2\text{ km}^2 to  m2\text{ m}^2 by multiplying by 1,00021,000^2 (1,000,000). Then, divide the resulting  m2\text{ m}^2 by 10,000 to find the number of hectares.