Squared & Cubic Units (Edexcel IGCSE Maths)

Spec point — 1.10B

Squared & cubic units

How do I convert between squared units (areas)?

• You need to square the unit conversion rates

  • E.g., 1 cm² = 10² mm² = 100 mm²
  • This is because area is 2D
  • The fact the units have a 'squared' on them will help you remember

• It can help to imagine a square

  • E.g. 1 m² is a square measuring 1 m × 1 m
  • In cm this would be 100 cm × 100 cm
  • So 1 m² is equivalent to 10 000 cm²

• The basic conversions for area are

  • 1 cm² = 100 mm²
  • 1 m² = 10 000 cm²
  • 1 km² = 1 000 000 m²

• You may be told conversions for other units in a question, such as

  • 1 hectare (ha) = 10 000 m²

How do I convert between cubed units (volume)?

• You need to cube the unit conversion rates

  • E.g. 1 cm³ = 10³ mm³ = 1000 mm³
  • This is because volume is 3D
  • The fact the units have a “cubed” on them will help you remember

• It can help to imagine a cube

  • E.g. 1 m³ is a cube measuring 1 m × 1 m × 1 m
  • In cm this would be 100 cm × 100 cm × 100 cm
  • So 1 m³ is equivalent to 1 000 000 cm³

• The basic conversions for volume are

  • 1 cm³ = 1000 mm³
  • 1 m³ = 1 000 000 cm³
  • 1 km³ = 1 000 000 000 m³

Worked Example Convert

(a) 8254 mm² to cm²

Answer:

1 cm = 10 mm

1 cm²= 10²mm²= 100 mm²

*8254 mm ² = (8254 ÷ 100) cm ² *

Final answer: 82.54 cm²

(b) 2.54 m³ to cm³

Answer:

1 m = 100 cm 1 m³= 100³cm³= 1 000 000 cm³

*2.54 m ³ = (2.54 × 1 000 000) cm ³ *

Final answer: 2 540 000 cm³