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Convert between metric units of length, area, and volume

Metric conversion involves interpreting prefixes as powers of ten and using equivalent relationships among common units of length (such as millimetres, centimetres, metres, and kilometres), area, and volume, including the relationship 1 L=1 dm31\text{ L}=1\text{ dm}^3. Because area measures two-dimensional extent and volume measures three-dimensional extent, conversion factors are squared or cubed respectively; the scope is common metric units and decimal quantities, not generalized dimensional analysis or compound-unit conversions such as speed or density.

Detailed Explanation: Convert between metric units of length, area, and volume

Metric prefixes tell you how large a unit is:

  • 1 m=100 cm1\text{ m}=100\text{ cm}
  • 1 km=1000 m1\text{ km}=1000\text{ m}
  • 1 cm=10 mm1\text{ cm}=10\text{ mm}

For length, use the conversion factor once. For area, square the factor because there are two dimensions. For volume, cube the factor because there are three dimensions.

Example: Convert:

  1. 2.4 m2.4\text{ m} to centimetres
  2. 0.35 m20.35\text{ m}^2 to square centimetres
  3. 1.8 L1.8\text{ L} to cubic centimetres

1. Convert length

Since 1 m=100 cm1\text{ m}=100\text{ cm}, multiply by 100100:

2.4 m×100=240 cm2.4\text{ m}\times 100=240\text{ cm}

So, 2.4 m=240 cm2.4\text{ m}=240\text{ cm}.

2. Convert area

For area, square the length conversion factor:

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

Now multiply:

0.35 m2×10,000=3500 cm20.35\text{ m}^2\times 10{,}000=3500\text{ cm}^2

So, 0.35 m2=3500 cm20.35\text{ m}^2=3500\text{ cm}^2.

3. Convert volume

Use the fact that:

1 L=1 dm31\text{ L}=1\text{ dm}^3

Also, 1 dm=10 cm1\text{ dm}=10\text{ cm}, so:

1 L=1 dm3=(10 cm)3=1000 cm31\text{ L}=1\text{ dm}^3=(10\text{ cm})^3=1000\text{ cm}^3

Now multiply:

1.8 L×1000=1800 cm31.8\text{ L}\times 1000=1800\text{ cm}^3

So, 1.8 L=1800 cm31.8\text{ L}=1800\text{ cm}^3.

Remember: use the factor once for length, square it for area, and cube it for volume.

Learn by doing: Convert between metric units of length, area, and volume

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