Surface Areas and Volumes • Topic 3 of 3

Conversion of Units

Why Convert Units?

In real-life problems, measurements may be given in different units. To calculate surface area or volume correctly, all measurements must be in the same unit system.

Length Conversions:

ConversionFormula
m to cmMultiply by 100
mm to cmDivide by 10
cm to mmMultiply by 10
km to mMultiply by 1000
m to kmDivide by 1000

Area Conversions (Square Units):

ConversionFormulaReason
m² to cm²Multiply by 10,000
mm² to cm²Divide by 1001 cm² = 10 mm × 10 mm = 100 mm²
km² to m²Multiply by 1,000,0001 km² = 1000 m × 1000 m = 1,000,000 m²

Volume Conversions (Cubic Units):

ConversionFormulaReason
m³ to cm³Multiply by 1,000,000
mm³ to cm³Divide by 10001 cm³ = 10 mm × 10 mm × 10 mm = 1000 mm³
litre (L) to cm³Multiply by 10001 L = 1000 cm³
m³ to litreMultiply by 10001 m³ = 1000 L

Quick Reference Table:

FromToMultiply by
cmm0.01
cm²10,000
cm²0.0001
cm³1,000,000
cm³0.000001
Surface Area & Volume — Sphere & HemisphererSphererHemisphereSphereHemisphereCurved SA4πr²2πr²Total SA4πr²3πr²Volume(4/3)πr³(2/3)πr³
1
Worked Example

Solve a standard problem on Conversion of Units.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Conversion of Units.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Tap an option to check your answer0 / 4
Q1.$1$ m equals:
Explanation: $100$ cm.
Q2.$1$ m$^2$ equals:
Explanation: $10000$ cm$^2$.
Q3.$1$ m$^3$ equals:
Explanation: $10^6$ cm$^3$.
Q4.$1$ litre equals:
Explanation: $1000$ cm$^3$.