Squared & Cubic Units (Cambridge (CIE) IGCSE International Maths)
Revision Note
Written by: Naomi C
Reviewed by: Dan Finlay
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
1 cm = 10 mm
1 cm2 = 102 mm2 = 100 mm2
8254 mm2 = (8254 ÷ 100) cm2 = 82.54 cm2
82.54 cm2
(b) 2.54 m3 to cm3
1 m = 100 cm
1 m3 = 1003 cm3 = 1 000 000 cm3
2.54 m3 = (2.54 × 1 000 000) cm3 = 2 540 000 cm3
2 540 000 cm3
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