Mini-Mods: General Chemistry - Units
Squared/Cubic Units
Squared and cubic units most often come up when dealing with units of area or volume respectively (although there are many other scientific quantities that also use units raise to some power). Remember that a unit operates mathematically like algebraic quantity – and this makes sense. If we’re talking about an area of a rectangle in m2 then the reason we have that quantity is because we multiplied the short length of the rectangle by the long length.
Similarly, with volume, three lengths are multiplied together, so the unit of volume must contain a length raised to the power of three (or length cubed) e.g. m3.
Squared/Cubic Unit Conversion
In order to perform a unit conversion containing squared or cubic units, we must consider there to be multiple units that each require converting. For example 4.00 cm2 should be interpreted as 4.00 (cm x cm). Breaking up the more complicated unit in this way, will make the conversion much easier. Then each individual unit will need its own conversion factor.
How many mm2are there in 4.00 cm2
First we break up the squared units and then introduce a conversion factor for every unit.
Practice Question 1
How many cm2 are there in 0.452 m2?
How many m3 are there in 0.539 km3
Following the same method as above, we first break up the cubed units. This time we will need three conversion factors.
Practice Question Answers
1) 4520 cm2