AQA · Mathematics · 8300
GCSE Maths: Units: converting areas
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions and answers for Units: converting areas (Corbettmaths Video 350), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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How many square centimeters are in 1 square meter?
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10,000 cm². (Since 1 m = 100 cm, so 1 m² = 100 × 100 = 10,000 cm²)
How many square millimeters are in 1 square centimeter?
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100 mm². (Since 1 cm = 10 mm, so 1 cm² = 10 × 10 = 100 mm²)
How many square meters are in 1 square kilometer?
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1,000,000 m². (Since 1 km = 1000 m, so 1 km² = 1000 × 1000 = 1,000,000 m²)
How many cubic centimeters are in 1 cubic meter?
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1,000,000 cm³. (Since 1 m = 100 cm, so 1 m³ = 100 × 100 × 100 = 1,000,000 cm³)
How many cubic millimeters are in 1 cubic centimeter?
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1,000 mm³. (Since 1 cm = 10 mm, so 1 cm³ = 10 × 10 × 10 = 1,000 mm³)
How many cubic centimeters equal 1 liter?
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1,000 cm³. (1 litre = 1,000 cm³)
How many milliliters equal 1 cubic centimeter?
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1 ml = 1 cm³. They are equivalent.
To convert from m² to cm², multiply by ?
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10,000
To convert from m³ to cm³, multiply by ?
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1,000,000
Why is the conversion factor for area (m² to cm²) different from the linear conversion factor (m to cm)?
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Because area is two-dimensional, you must square the linear conversion factor. For example, 1 m = 100 cm, but 1 m² = 100 × 100 = 10,000 cm².
Why is the conversion factor for volume (m³ to cm³) different from the linear conversion factor (m to cm)?
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Because volume is three-dimensional, you must cube the linear conversion factor. For example, 1 m = 100 cm, but 1 m³ = 100 × 100 × 100 = 1,000,000 cm³.
If a tile measures 20 cm by 20 cm, what is its area in square centimetres?
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400 cm². Area = 20 × 20 = 400 cm².
A floor measures 3 m by 5 m. What is the floor area in square metres?
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15 m². Area = 3 × 5 = 15 m².
A floor area is 15 m². How many square centimetres is this?
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150,000 cm². 15 × 10,000 = 150,000 cm².
How many 400 cm² tiles are needed to cover 150,000 cm²?
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375 tiles. 150,000 ÷ 400 = 375.
If tiles are sold in boxes of 10 and you need 375 tiles, how many boxes must you buy?
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38 boxes. 375 ÷ 10 = 37.5, so you must round up to 38 whole boxes.
What is the formula for the area of a circle in terms of radius r?
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A = πr², where π ≈ 3.14159.
How do you find the radius of a circle if you know its area A?
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Rearrange A = πr² to get r = √(A/π).
What is the relationship between the diameter and radius of a circle?
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Diameter = 2 × radius, or d = 2r.
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