Capacity and Volume Conversion

Lesson 4: Conversions Between SI and Imperial - Capacity and Volume Conversions

   Constructing Knowledge

Volume is the measure of the amount of space an object takes up. Capacity is the measure of the liquid an object can hold. The base SI unit for capacity is the litre and the base SI unit for volume is the cubic metre (m³).

Imperial units for capacity vary depending upon whether the measurement is from the US (United States) Imperial system or the UK (United Kingdom) Imperial system. As the use of these units moved from Europe to the United States in the 18th century, small differences exist in many of the measurements. Some measurements, like the pound, were eventually standardized between the US and UK Imperial systems, but some, mostly for capacity, remain different.

The conversion ratios within each Imperial system are the same (4 quarts = 1 gallon) however the relative sizes of the US gallon and the UK gallon are different. You can see this when looking at the conversion factors in litres. The US gallon is equivalent to 3.79 litres and the UK gallon is equivalent to 4.545 litres.

Capacity and Volume: Imperial to SI Imperial SI 1 UK gallon 4.546 litres 1 US gallon 3.79 litres 1 cubic inch 16.39 cubic centimetres 1 cubic yard 0.765 cubic metres 1 US cup 237 mL 1 UK pint 568 mL 1 US pint 473 mL

Capacity and Volume: Imperial to SI SI Imperial 1 litre 0.220 UK gallons 1 litre 0.264 US gallons 1 cubic centimetre 0.061 cubic inches 1 cubic metre 1.308 cubic yards SI Capacity Measure 1 metric cup 250 mL

When doing capacity and volume conversions, ensure you are using the correct conversion ratio.

   Multimedia

A video demonstrating capacity conversion between the SI and Imperial system is provided.

EXAMPLE 1

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A gas tank in a large car has a capacity of 60 litres. What is the capacity of the gas tank, in UK gallons?

Solution

\(\begin{align} \frac{y}{60\,\text{L}}&=\frac{1\,\text{UK gal}}{4.546\,\text{L}} \\ \\ \frac{y}{\cancel{60\,\text{L}}}\times {\color{red}{\cancel{60\,\text{L}}}}&=\frac{1\,\text{UK gal}}{4.546\cancel{\text{L}}}\times {\color{red}{60\cancel{\text{L}}}} \\ \\ y&=\frac{1\,\text{UK gal}\times 60}{4.546} \\ \\ y&=\frac{60\,\text{UK gal}}{4.546} \\ \\ y&=13.2\,\text{UK gal} \\ \end{align}\)

The gas tank has a capacity of approximately 13.2 UK gallons.

EXAMPLE 2

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A gas tank in a large car has a capacity of 60 litres. What is the capacity of the gas tank, in US gallons?

Solution

\(\begin{align} \frac{y}{60\,\text{L}}&=\frac{1\,\text{US gal}}{3.79\,\text{L}} \\ \\ \frac{y}{\cancel{60\,\text{L}}}\times {\color{red}{\cancel{60\,\text{L}}}}&=\frac{1\,\text{US gal}}{3.79\cancel{\text{L}}}\times {\color{red}{60\cancel{\text{L}}}} \\ \\ y&=\frac{1\,\text{US gal}\times 60}{3.79} \\ \\ y&=\frac{60\,\text{US gal}}{3.79} \\ \\ y&=15.8\,\text{US gal} \\ \end{align}\)

The gas tank has a capacity of approximately 15.8 US gallons.




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