Units resulting from a formula or Graph

In all our years of learning maths, we've learnt how to make all kinds of calculations. However, if I told you the answer is $42$42, your initial response may be, "$42$42 what?" That's why units of measurement are really important!

We can use units of measurement to define any physical phenomenon, such as quantities, weights, lengths, areas, volumes and rates. Let's look at some different units of measurement now.

 

Measurements of Length

Length (distance) is a measurement of one dimension. For example, we could measure from one point to another

Units of measurements for length include millimetres ($mm$mm), centimetres ($cm$cm), metres ($m$m) and kilometres ($km$km).

 

Measurements of Area

Area is a measure of two dimensions: length and width. Hence, it is measured in square units.

Units of measurements for area include square millimetres ($mm^2$mm2), square centimetres ($cm^2$cm2), square metres ($m^2$m2) and hectares ($ha$ha).

 

Measurements of Volume

Volume is a measure of three dimensions: length, width and height. Hence, it's measured in cubed units.

Units of measurements for volume include millimetres cubed ($mm^3$mm3), centimetres cubed ($cm^3$cm3), metres cubed ($m^3$m3)

Measurements of Mass

Units of measurement for mass include grams (g), kilograms (kg) and tonnes (t).Mass is a measure of how heavy something. We often refer to the mass of an object as its weight.

 

 

 

Measurements of Capacity

Capacity is a measure of how much something holds, such as how much liquid will fit in a bottle.

Measures of capacity include millilitres (ml) and litres (l).

 

 

Measurements in Rates

A rate is a ratio between two measurements with different units. There are any number of combinations of measurement units for rates, such as dollars per kilogram ($/kg), kilometres per hour (km/h) and so on.

 

 

Units from Formula

Any formula whose components are measurements will have units attached to each of the pronumerals.

Here is a formula we a familiar with, the speed of an object is a measure of the distance traveled per unit of time.  

$S=\frac{d}{t}$S=dt​

 The units for Speed in the formula are derived from the units used for distance and time.  So if the distance is measured in kilometres and time is measured in hours, then the 

$\text{Speed (unit) }=\frac{\text{distance (units) }}{\text{time (unit) }}$Speed (unit) =distance (units) time (unit) ​

$\text{Speed (unit) }=\frac{\text{kilometres }}{\text{hour }}$Speed (unit) =kilometres hour ​

$\text{Speed (unit) }=\text{kilometres / hour }$Speed (unit) =kilometres / hour

 

Worked Examples

Question 1

 

Question 2