How to calculate the volume of a country

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

18 February 2024

Kaggai Thiong’o was not convinced by the method I use last week in calculating the mass of Kenya. He writes: “When you compute the mass against surface areas you get it wrong. I assume you should use volume. But how do you get the volume of Kenya?”

As explained last week, the portion of the Earth that belongs to Kenya is all the underground material going right to the centre of the planet. If it is cut out, it would have an inverted pyramidal or conical shape with a somewhat flat top and a sharp point at the bottom.

The question Kaggai is asking is what is the volume of such a shape? It is easier to start by looking at a simpler shaped solid…the simplest is a cone. The volume of a cone is one-third that of a cylinder of similar radius and height. But the volume of a cylinder is directly proportional to the area of its flat, circular surface.

So, it follows that the volume of a cone is also directly proportional to the area of the flat base. The same applies to the volume of a pyramid. Therefore, to find the volume of a country, we only need to know what fraction of the earth’s surface area it occupies: that will be the same fraction of the volume.

And, as Kaggai correctly notes, the mass is proportional to the volume; but the volume is proportional to the surface area. Consequently, the mass is proportional to the surface area. That is what I did last week.

To answer Kaggai’s direction question, we start by finding the volume of the earth. Its radius is about 6,400km, so the volume is approximately one trillion cubic kilometres. Don’t worry if you have forgotten the formular for calculating volume of a sphere: even school children are not expected to remember it! It is given in the booklet of standard mathematical tables that is always issued to KCSE candidates.

Last week, we found that Kenya’s surface area is 0.00114 that of the earth. Kenya’s volume is also the same fraction of the one trillion cubic kilometres of the earth. Therefore, we own about 1.14 billion cubic kilometres of the material that makes up this planet.

Now that we know how far underground our territory extends, we should ask how high upwards does our airspace go? Is it to the end of the atmosphere? How many kilometres up is that?