Radiation machines used to treat tumors produce an intensity

Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity of at a distance of 2.5 meters?

Solution

intensity of radiation that varies inversely as the square of the distance from the machine.

Let intensity of radiation be I and distance be d.

We can write relations: I = k/d^2 wher k is a constant

d=3 mt ; I = 62.5 milliroentgens per hour;

62.5 = k/3^2---> k = 562.5

I = 562.5/d^2

Nowe find I when d=2.5mt

I = 562.5/2.5^2 = 90 milliroentgens per hour