Volume
Example 1: Concrete slab
How much cement-based filler do you need to lay on top of a concrete subfloor if the average thickness is going to be 25 mm and the slab measures 12 m by 3.5 m?
Notice that there is a combination of units here - the length and width are in metres and the thickness is in millimetres. So the first thing we need to do is convert the thickness to metres: 25 mm = 0.025 m3
Now we can do the calculation.
Volume = length x width x thickness
= 12 m x 3.5 m x 0.025 m
= 1.05 m3
In practice, you might add 10% to cover variations in the original subfloor level which will affect the thickness of your filler. So in this case you would add 0.105 m3 to the total.
Example 2: 2-stroke fuel
A common petrol:oil ratio for 2-stroke engines is 25:1. This means that for every 25 parts of petrol you need to mix in 1 part of 2-stroke oil.
If you had a 4 litre container of petrol, how much oil do you need to add?
We know that:
1 L = 1000 mL, so
4 L = 4,000 mL.
Therefore the calculation will be as follows.
4,000 mL (petrol) ÷ 25 = 160 mL (2-stroke oil).
Example 3: Water tank
How much water can a tank hold with a diameter of 1800 mm and a height of 1500 mm?
Here is the calculation.
Cylinder volume = area of circle (cross section) x height
= diameter x diameter x 3.14 x height
2 2
= 1.8 ÷ 2 x 1.8 ÷ 2 x 3.14 x 1.5
= 0.9 x 0.9 x 3.14 x 1.5
= 3.815 m3
Since there are 1000 litres in 1 m3, the volume in litres is:
3.815 m3 x 1000 = 3815 L
Learning activity
Audio 7 (mp3 |6|KB)1. You are landscaping your front yard and have decided to spread topsoil over the lawn area. The topsoil will be an average of 50 mm thick, and needs to cover an area of 7 m by 8.5 m.
How much topsoil will you need?
Dimensions | Value |
---|---|
Length in metres | 8.5 |
Width in metres | 7 |
Thickness in metres | 0.05 |
Volume in cubic metres (Length x Width x Thickness) | 2.975 |
2. You also want to put a water feature pond at one end of the yard. The pond will be round, with a diameter of 1.8 metres. The depth will be 200 mm. How much water will the pond hold when it is full?
Dimensions | Value |
---|---|
Surface area which is Diameter ÷ 2 x Diameter ÷ 2 x 3.14 | 2.543 |
Depth in metres | 0.2 |
Volume in cubic metres which is Surface area x Depth | 0.509 |
Volume in litres | 509 |