## Lesson 11: Volume of Solids (I)

May 31, 2012

Vocabulary on Volume of Solids

Volume Worksheet

Volume Word Problems

I Have to Know by the End of this Lesson

### 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.

### 2.1 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.

 Volume units m3 dm3 cm3 Capacity units kl hl dal l dl cl ml

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.

 Volume units m3 dm3 cm3 Capacity units kl hl dal l dl cl ml Mass units t q mag kg dag hg g

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: