Conversions of Area and Volume

Converting area and volume measurements are an essential skill in Mathematics. These types of calculations are straightforward once you understand the basic metric units of measurement. Below is a guide to help you navigate through these conversions with clarity and examples.

Converting Area

Area is a measurement of the surface of a two-dimensional shape. When converting area, remember that the measurement is always in square units (e.g. cm², m²), as it represents a 2D space. The key principle to remember is that when you are converting between different units for area, you are working with squared values.

Example 1: Converting m² to cm²

Let’s look at how you would convert 1 square metre (1m²) to square centimetres (cm²).

1. Start with the definition of 1m². It represents an area of 1 metre by 1 metre.
   • In equation form: 1m² =1m×1m 
2. Now, we know that 1 metre is equal to 100 centimetres. Therefore, to convert 1 metre to centimetres:

1m=100cm

3. Next, substitute the value of 1m with 100cm into the equation:

                                             1m² =100cm×100cm 

Perform the multiplication:

1m² =10,000cm²

So, 1 square metre is equal to 10,000 square centimetres (1m² = 10,000cm²).

Example 2: Converting 3m² to cm²

To convert 3 square metres to square centimetres:

1. First, recall that 1m² = 10,000cm².
2. Multiply 3 by 10,000: 

3m² = 3×10,000cm²  =30,000cm² 

Thus, 3 square metres is equal to 30,000 square centimetres.

Converting Volume

Volume measures the amount of space occupied by a three-dimensional object. When converting volume, remember that you are working with cubic units (e.g. cm³, m³), as volume involves three dimensions.

Example 1: Converting m³ to cm³

Let’s now look at how to convert 1 cubic metre (1m³) into cubic centimetres (cm³).

1. Start with the definition of 1m³. It represents a cube with each side measuring 1 metre.
   • In equation form: 

               1m³ = 1m x 1m x 1m

Since we know that 1 metre equals 100 centimetres, substitute 100cm for each metre:

                                             1m³ = 100m x 100m x 100m

2. Multiply the three values together:

1m³ = 1,000,000cm³

Therefore, 1 cubic metre is equal to 1,000,000 cubic centimetres (1m³ = 1,000,000cm³).

Example 2: Converting 2m³ to cm³

To convert 2 cubic metres to cubic centimetres:

1. Recall that 1m³ = 1,000,000cm³.
2. Multiply 2 by 1,000,000: 

2m³ = 2×1,000,000cm³ = 2,000,000cm³

Thus, 2 cubic metres is equal to 2,000,000 cubic centimetres.

General Conversion Formula

To generalise, when converting between different units of area or volume, remember:

• For area:

1m² =10,000cm² (since 1m = 100cm)

• For volume:

1m³ = 1,000,000cm³ (since 1m = 100cm)

Additional Examples

Example 3: Converting 5m² to mm²

1. We know that 1m = 1000mm.
2. So, 1m² = 1000mm × 1000mm = 1,000,000mm².
3. To convert 5m², multiply 5 by 1,000,000: 

5m² = 5×1,000,000mm² = 5,000,000mm²

Thus, 5 square metres is equal to 5,000,000 square millimetres.

Example 4: Converting 0.5m³ to cm³

1. Recall that 1m³ = 1,000,000cm³.
2. Multiply 0.5 by 1,000,000: 

0.5m³ = 0.5 x 1,000,000cm³ = 500,000cm³

Thus, 0.5 cubic metres is equal to 500,000 cubic centimetres.

By understanding the principles of converting area and volume and practising these types of conversions, you'll find it much easier to solve problems that involve changing between metric units. Keep these conversions and the key differences between square and cubic units in mind, and practice with a variety of examples to solidify your skills.

For more information about area and shapes visit our Geometry and measures section.