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Converting square and cubic metric measures

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Last updated 26 October 2012 15:30 by NZTecAdmin

One of the challenges facing automotive, building and other trades learners and tutors is understanding and teaching the relationship between linear metric measure conversions (converting between mm and m) and square (mm2 and m2) and cubic (mm3 and m3) metric conversion. This resource describes two approaches to expressing a volume in cubic centimetres (cc) or litres, given the linear measurements in mm.

Calculating engine capacity

Consider this diagram of an engine cylinder for a S50B32 6-inline cylinder BMW car engine, with a capacity of 3201cc or 3.2L:

The cylinder is one of six in a 6-cylinder engine. The task is to calculate the volume of the cylinder in cubic centimetres (cc) and use that to find the engine capacity in litres.

Assuming the cylinder has already had its dimensions measured . . .

So which is the ‘best’ approach for learners?

There are some learners who could do both, and there are others who struggle with multiplying to arrive at a reasonable answer. But it seems the safer option (and certainly with less to consider) is to go with the second approach – convert first then calculate.

The conversion, 1cm = 10mm, seems much more accessible [Measurement Step 4] than the downstream conversion, 1cm3 = 1000mm3 [Measurement Steps 5 to 6]

However there is opportunity to build number sense and problem solving skills by using the first approach. Learners can formulate the conversion factor for mm3 to cm3 and they could use that same logic and sequencing to work out the conversion factor between, for example, mm3 and m3.

Key numeracy outcomes

Working through this contextual problem can build learners' ability to:

  • write and understand exponents as they are used with metric and other units, eg., squared terms (cm2) and cubed terms (cm3)
  • multiply and divide decimal numbers by 10 and 1000 to assist with converting between mm and cm, and between cm3 and litres.
  • Use a calculator (with reasonableness) to work out circle areas and cylinder volumes to an appropriate accuracy
  • Become familiar with converting between metric and imperial units, when the context demands.
  • understand how 2- and 3-dimensional units of measure relate to linear measure.



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