Expert: Josh - 10/11/2005

Question
How many litres of water would be in a tank that was 10,000m2 with 80cm depth?

Answer
Hi Alana,

To answer this question, we need to understand the relationship between density and fluid volume.

Water has a density of 1.0 grams/millilitre [g/mL], that is to say, 1 cubic centimetre (cm^3) of H2O weighs 1 g.

The unit "milli" as in "milli-litre" is one thousandth of a litre. i.e., 1000 mL = 1 L.

Now, let's calculate the volume of the tank.
Its area is 10,000 m^2.
Since 100 cm = 1 m, in terms of area, (100)*(100) cm^2 = 1 m^2.
Therefore, 10,000 m^2 = 10000*10000 cm^2.

Area multiplied by depth gives volume. So, vol. of tank equals 10000*10000*80 cm^3 (read "cubic cm"). [#1]

It's important that we consistently use the same units in all calculations.

From [#1], we have 8,000,000,000 cm^3 of volume.
Since 100*100*100 cm^3 = 1 m^3, we have 8000 litre of capacity.

So, the tank can hold 8000 L of water.

Note: To go between different units, always start from first principle. Start with simple conversions.

e.g., 100 cm = 1 m. This is a measurement of length, right?

To turn this into one unit of area, square both sides.
100*100 cm^2 = 1*1 m^2, => 10000 cm^2 = 1m^2. Now we are in two dimension.

To turn this into one unit of volume, we follow the same idea, 100*100 [cm^2] * 100 c[m] = 1 [m^2] * 1 [m].
Therefore, 1000000 cm^3 = 1 m^3.

Hope this helps:)