How to calculate the volume of water containers

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

19 July 2009

How can one measure the volume of a water container in litres? This seemingly uninteresting question has suddenly become important to Nairobians and other urbanites in Kenya. The prevailing water shortage has meant that people have to account for virtually every drop used in the house.

The answer to the question depends on the shape of the container. If it is a cuboid (that is, all the sides are rectangular and all angles are 90 degrees), then the solution is simple. First, you measure the dimensions of the container – length, width and height – in centimetres. Second you multiply out the three measurements. This gives you the volume in cubic-centimetres, or “cc”.

Finally you divide the cubic-centimetres by 1,000 to get the number of litres. Now this comes as a shock to many people because if you have a seemingly “small” container measuring just one metre on all sides, its volume would be 1,000 litres! If doubt it, do the math.

If the container is not a cuboid, then the above method will NOT work. Most water jerry cans are cylindrical and for this shape, the volume is determined by multiplying the area of the base by the height.

The base of a cylinder is circular thus its area is given by pi (3.14) times the square of the radius. Now don’t confuse “radius” with “diameter” or with “circumference”. The circumference is the length along the edge of the circle; the diameter is the distance from on end, through the centre, to the other end; the radius is the length from the edge to the centre.

Thus the steps to be followed in determining the volume of a cylindrical container are as follows: first, measure the diameter of the circular part (distance from end to end) in centimetres. Second, divide this measurement by two. Third, multiply the result by itself (that is, square it). Fourth, multiply the answer from the third step by pi (3.14).

So far, what you have is the area of the base. Now measure the height of the container, also in centimetres and multiply it by the area. Finally, divide the answer by 1,000 to get the number of litres. QED!

Buckets are funny. Their base is usually smaller than their mouth. Therefore the above method will not work. A small variation is required: instead of measuring the diameter of the base alone, measure that of the mouth as well and find the average. Then use this average value in the formula of a cylinder.

Two interesting observations come out of this exercise: First is the convenience of the metric system of measurements (metres, centimetres, litres etc) over the imperial one (inches, feet, gallons etc). If the dimensions of the container were measured in inches, for example, it would not be as easy to convert from cubic-inches to gallons. The conversion factor is 277.274 cu-in per gallon!

Secondly, if the base diameter of a cylindrical container is doubled, the volume does not double: it goes up by a factor of four! Thus a jerry can with a base diameter of 40cm and a height of 75cm will be approximately 100L in capacity, while another one of the same height (75cm) but an 80cm base will be 400L…Not 200L!