Lesson 11: Volume of Solids (I)May 31, 2012
1. Volume of a solid
1.1. Volume units
Volume is length by length by length, so the basic unit of volume is a cube with edge length one metre. Its volume is 1 metre × 1 metre × 1 metre, which is written m3 (cubic metre).
The basic unit of volume is the cubic metre, which is written m3.
Multiples and submultiples of cubic metre are the following:
|unit||it is the volume of a||it equals||symbol|
|multiples||cubic kilometre||cube whose edges measure one kilometre||1000000000 m3||km3|
|cubic hectometre||cube whose edges measure one hectometre||1000000 m3||hm3|
|cubic decametre||cube whose edges measure one decametre||1000 m3||dam3|
|base unit||cubic metre||cube whose edges measure one metre||m3|
|submultiples||cubic decimetre||cube whose edges measure one decimetre||0.001 m3||dm3|
|cubic centimetre||cube whose edges measure one centimetre||0.000001 m3||cm3|
|cubic millimetre||cube whose edges measure one millimetre||0.000000001 m3||mm3|
You have to bear in mind that volume units are cubes and three-dimensional. The conversion of a unit into another one is done by dividing or multiplying both the length, the height and the width, that is dividing and multiplying by ten three times; in other words, dividing and multiplying by 1000.
The volume units go up by a factor of 1000 at the time.
Each jump to a smaller unit is equivalent to multiply by 1000, you have to move the decimal point three places to the right. Each jump to a larger unit is equivalent to divide by 1000, you have to move the decimal point three places to the left. Here you are a sketch:
Now you can practice on the following links:
1 – Volume unit conversion. (with hints)
1.2 Volume of an object
Volume of an object is the amount of space it occupies.
We will begin by a basic solid, the cube.
2. Relationships among volume, capacity and mass
2.1 Volume and capacity
The capacity of a container is known as the volume of the liquid or gas that it can hold.
Capacity and volume have equivalent meanings. Establishing a special unit to measure volume isn’t necessary, so using the cubic metre would be enough, but for practical use the litre was established as a unit. If you pour one litre in a cube with an edge of 1 dm it will fit in the cube exactly.
The litre is identical to the cubic decimetre (dm³), although it wasn’t always so . Recall
The litre is the capacity of a cubic decimetre.
We know 1 dm is 0·1 m or 10 cm, so 1 dm³ is 10×10×10 cm:
This, of course, means that there are 1,000 cm³ in a litre, or that 1 cm³ is equal to 1 mL.
The following table shows the equivalence between volume units and capacity units.
2.2. Volume, mass and capacity
A recipient contains a litre of pure water, which occupies 1 dm3. We weight it and it weights 1 kilogram exactly.
One kilogram is the weight of 1 dm3 of pure water.
If we weigh a container with 1 ml of pure water with, which occupies 1 cm3, it weights 1 gram.
One gram is the weight of 1 cm3 of water
The following table shows the equivalence among volume units, capacity units and mass units for pure water.
1 l =1 dm3 = 1 kg of pure water
NOTE: If we have other substance different from pure water one litre doesn’t weight one kilo.
In the following video you can find a long explanations about these topics: