4.11 J) Changing Units: Area & Volume – Part 2

**Example 1**

Convert 25 m^{2} into cm^{2}.

Both of the quantities above are about area. We know that this is the case because both of the units are squared (m^{2} and cm^{2}). We are being asked in the question to convert metres into centimetres. There are 100 cm in 1 metre. Therefore, the length scale factor is 100.

We are working with area and we know that the area scale factor is the square of the length scale factor.

Therefore, the area scale factor is 10,000.

We are going from a larger unit (metres) to a smaller unit (cm). This means that we multiply the area (25) by the area scale factor (10,000).

The area in square centimetres is 250,000 cm^{2}.

**Another Method**

There is another way to convert the area from one unit to another. This method involves multiplying or dividing by the conversion the number of times in the power.

For the above example, we were converting metres into centimetres, and we are able to convert metres into centimetres by multiplying by 100. The power in the units was 2 (cm^{2}/ m^{2}). Therefore, we multiply 25 by 100 two times.

Therefore, the area in centimetres is 250,000 cm^{2}. This is the same answer that we found when using the previous method.

**Example 2**

Convert 280 mm^{3} into cm^{3}.

The quantities in the question are volumes. Therefore, we will be using the volume scale factor. We know that the volume square factor is the cube of the length scale factor. There are 10 mm in a cm. Therefore, the length scale factor is 10. We are now able to work out the volume scale factor by cubing the length scale factor.

The volume scale factor is 1,000.

We are converting a smaller unit into a larger unit (we are going from mm to cm). This means that we divide our volume (280) by our volume scale factor (1,000).

Therefore, the volume in centimetres is 0.28 cm^{3}.

**Other Method**

I am now going to use the other method. In this question, we are converting millimetres into centimetres and we would do this for a length by dividing by 10. The power in the units is 3. Therefore, we divide the volume (28) by 10 three times. The working is shown below:

This tells us that the volume in centimetres is 0.28 cm^{3}.

**End Note**

I would recommend trying both methods that have been discussed in this section to see which method you prefer. The quiz has some questions that you can try both methods on. There are also worked solutions for both of the methods.