Converting Compound and Area-Volume Units

Square the conversion factor for lengths.

1. Since 1 m is 100 cm, 1 m^2 is 100^2=10000 cm^2.
2. Therefore 0.6\times10000=6000 cm^2.

Use the area conversion factor, not the length conversion factor.

1. There are 10000 cm^2 in 1 m^2.
2. Divide by 10000: 75000\div10000=7.5 m^2.

Cube the conversion factor for lengths.

1. Since 1 m is 100 cm, 1 m^3 is 100^3=1000000 cm^3.
2. Therefore 0.004\times1000000=4000 cm^3.

Use the volume of one litre in cubic centimetres.

1. One litre is 1000 cm^3.
2. Therefore 8600\div1000=8.6 litres.

A square centimetre contains a square array of square millimetres.

1. Since 1 cm is 10 mm, 1 cm^2 is 10^2=100 mm^2.
2. Therefore 250\div100=2.5 cm^2.

Convert the distance travelled in one hour from metres to kilometres.

1. In one hour the distance is 18\times3600=64800 m.
2. Divide by 1000 to get 64.8 km/h.

Convert kilometres to metres and hours to seconds.

1. 54 km is 54\times1000=54000 m, and 1 hour is 60\times60=3600 seconds.
2. So the speed is 54000 m in 3600 s: 54000\div3600=15 m/s.

Convert the volume unit and the mass unit separately.

1. One cubic metre contains 1000000 cm^3, so its mass is 2700000 g at this density.
2. This is 2700 kg, giving a density of 2700 kg/m^3.

A cubic metre contains a million cubic centimetres.

1. 920 kg is 920000 g, and 1 m^3 is 1000000 cm^3.
2. The density is 920000\div1000000=0.92 g/cm^3.

Find the volume in one minute, then convert cubic centimetres to litres.

1. In one minute the volume is 120\times60=7200 cm^3.
2. This is 7200\div1000=7.2 litres per minute.

Convert to square metres first, then use the square of the kilometre conversion factor.

1. The area is 4.2\times10000=42000 m^2.
2. One square kilometre is 1000^2=1000000 m^2.
3. Therefore the field area is 42000\div1000000=0.042 km^2.

Convert the volume to cubic centimetres, then divide by the number of seconds in a minute.

1. 0.45 litres is 450 cm^3.
2. The flow rate is 450\div60=7.5 cm^3/s.

Find the mass of one square metre of card first.

1. Since 1 m is 100 cm, 1 m^2 is 100^2=10000 cm^2.
2. So one square metre of card has mass 0.025\times10000=250 g.
3. 250 g is 0.25 kg, so the card is 0.25 kg/m^2.

Consider how many square centimetres there are in one square metre.

1. One square metre contains 10000 cm^2.
2. The force on that area at this pressure is 3.2\times10000=32000 N.
3. The pressure is 32000 N/m^2.

Convert the required area into the same units as the quoted area.

1. 0.75 m^2 is 7500 cm^2.
2. This is 7500\div2500=3 times the quoted area.
3. The cost is 3\times8=£24.

Find the volume wasted in a year in cm^3, then change it to m^3.

1. Minutes in a year: 60\times24\times365=525600.
2. Water wasted in a year: 12\times525600=6307200 cm^3.
3. 1 m^3 is 100^3=1000000 cm^3, so this is 6307200\div1000000=6.3072 m^3.
4. Cost: 6.3072\times2.50=15.768, which is £15.77 to the nearest penny.

Convert the panel area before using the mass per unit area.

1. 8000 cm^2 is 0.8 m^2.
2. The mass is 4.5\times0.8=3.6 kg.
3. This is 3600 g.

Convert both flow rates to litres per hour before subtracting.

1. For A, 18\times60=1080 litres per hour.
2. For B, 250 cm^3/s is 0.25 litres per second, or 0.25\times3600=900 litres per hour.
3. The difference is 1080-900=180 litres per hour.

Change the volume to m^3 so that it matches the units of the density.

1. The volume of the plate is 40\times25\times0.8=800 cm^3.
2. 1 m^3 is 100^3=1000000 cm^3, so 800 cm^3 is 800\div1000000=0.0008 m^3.
3. Mass is density multiplied by volume: 7850\times0.0008=6.28.
4. The mass of the plate is 6.28 kg.

Convert the rainfall depth to metres before calculating a volume.

1. 18 mm is 0.018 m, so the volume collected in one hour is 0.018\times2500=45 m^3.
2. This is 45000 litres per hour.
3. Divide by 3600 to convert hours to seconds.
4. The collection rate is 45000\div3600=12.5 litres per second.