Question

The amount of bacteria in a certain glass box varies directly with the volume of the box and inversely with temperature of its surrounding. there are 3.6 million bacteria found in 9" by 4" by 5" rectangular prism at 250K. How many bacteria of the same kind will there be if the box is reduced into a cube with one side equal to 3 inches at 400K?

Answer 1

Let indicate the number of bacteria and indicate the volume of the glass and indicate the temperature.

Since, then is a constant and again then is a constant, Combining this we get is a constant or

3.6 million
million	cubic inches

From the above table we can calculate the number of bacteria i.e, as follows

Therefor the number of bacteria present in a box whose volume is reduced to a cube of inches side at is millions approximately.