Area and Volume Unit Conversions

The area of a square is side length times side length, so use the sides in centimetres.

There are 10\,000 cm² in 1 m², not 100.

Square metres are bigger than square centimetres, so the number gets smaller.

A square with sides of 1 cm has sides of 10 mm.

A cube with edges of 1 cm has edges of 10 mm.

Think about the side of a square: 1 m is 100 cm and 1 cm is 10 mm.

Part (a)

1. 1 m² =100\times100=10\,000 cm².
2. 2.3\times10\,000=23\,000, so 2.3 m² =23\,000 cm².

Part (b)

1. 1 cm² =10\times10=100 mm², so divide by 100.
2. 650\div100=6.5, so 650 mm² =6.5 cm².

The volume of a cube is length × width × height, so use the edges in centimetres.

1. Volume =100\times100\times100 cm³.
2. 100\times100=10\,000 and 10\,000\times100=1\,000\,000.
3. So 1 m³ =1\,000\,000 cm³.

There are 1\,000\,000 cm³ in 1 m³, and m³ are much bigger, so the number gets smaller.

1. 1 m³ =100\times100\times100=1\,000\,000 cm³, so divide by 1\,000\,000.
2. 600\,000\div1\,000\,000=0.6, so the volume is 0.6 m³.

A cube with edges of 1 cm has edges of 10 mm, so work out how many mm³ make 1 cm³.

1. 1 cm³ =10\times10\times10=1000 mm³, so divide by 1000.
2. 7500\div1000=7.5, so 7500 mm³ =7.5 cm³.

Litres are bigger than cubic centimetres, so the number of litres is the smaller number.

Part (a)

1. Each litre is 1000 cm³, so multiply by 1000.
2. 3.2\times1000=3200, so 3.2 litres =3200 cm³.

Part (b)

1. Litres are bigger than cm³, so divide by 1000.
2. 850\div1000=0.85, so 850 cm³ =0.85 litres.

Either change both lengths into centimetres first, or find the area in m² and then change it.

1. In centimetres the rug is 240 cm by 150 cm.
2. Area =240\times150=36\,000 cm².
3. Check: 2.4\times1.5=3.6 m², and 3.6\times10\,000=36\,000 cm².

Both lengths must be in metres before you multiply.

1. Change 40 cm into metres: 40\div100=0.4 m.
2. Area =3\times0.4=1.2 m².
3. Multiplying 3\times40=120 would mix two different units.

Change every area into cm² so you can compare them.

1. 0.4 m² =0.4\times10\,000=4000 cm².
2. 380\,000 mm² =380\,000\div100=3800 cm².
3. 0.04 m² =0.04\times10\,000=400 cm².
4. In order: 400, 3500, 3800, 4000 cm². The largest is 0.4 m².

Work out the volume in cm³ first, then change it into litres.

1. Volume =50\times30\times40=60\,000 cm³.
2. 60\,000\div1000=60, so the tank holds 60 litres.

Find the volume of the tank in m³, change it into litres, then take away what was used.

1. Volume =2\times1.5\times1=3 m³.
2. 3 m³ =3\times1000=3000 litres.
3. 3000-800=2200 litres are left.

Find the area of the floor in cm² first, and remember that Kim can only buy whole tiles and whole packs.

1. Area of floor =4.2\times3.5=14.7 m².
2. 14.7 m² =14.7\times10\,000=147\,000 cm².
3. 147\,000\div1800=81.66..., so Kim needs 82 tiles.
4. 82\div8=10.25, so 10 packs are not enough.
5. Kim needs to buy 11 packs.

The water forms a cuboid with the same base as the tank.

1. 120 litres =120\times1000=120\,000 cm³.
2. Area of the base =80\times50=4000 cm².
3. Depth =120\,000\div4000=30 cm.

Write all three lengths in centimetres, find the volume, then change it into litres.

1. 1.2 m =120 cm.
2. Volume =120\times80\times50=480\,000 cm³.
3. 480\,000\div1000=480 litres.
4. 480\div12=40 minutes.

Change the amount of soap into millilitres, then think about what to do with a part bottle.

1. 0.03 m³ =0.03\times1000=30 litres.
2. 30 litres =30\times1000=30\,000 ml.
3. 30\,000\div350=85.71...
4. Only whole bottles count, so 85 bottles can be filled completely.

Change the volume of the tank into litres before you take anything away.

Part (a)

1. Volume of the tank =1.5\times1\times0.8=1.2 m³ =1200 litres.
2. Water pumped out =25\times24=600 litres.
3. 1200-600=600 litres are left.

Part (b)

1. 600 litres =600\times1000=600\,000 cm³.
2. The base is 150 cm by 100 cm, so its area is 15\,000 cm².
3. Depth =600\,000\div15\,000=40 cm.