Question

Radiation machines used to treat tumors produce an intensity of radiation that variesinversely as the square of the distance from the machine. At 3 meters, the radiationintensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.6 meters?The intensity is(Round to the nearest tenth as needed.)

Answer 1

Answer: Intenisy = 83.2 milliroentgens per hour

Let the intensity from the radiation = I

Let the distance = d

The intensity is inversely proportional to the square of its distance

`\begin{gathered} I\text{ }\propto\text{ }(1)/(d^2) \\ \text{Introducing a proportionality constant} \\ I\text{ = }\frac{k\text{ x 1}}{d^2} \\ I\text{ = }(k)/(d^2) \\ \text{When I = 62.5 , d = 3} \\ \text{From the above equation} \\ K=I\cdot d^2 \\ K\text{ = 62.5 }\cdot(3)^2 \\ K\text{ = 62.5 x 9} \\ K\text{ = 562.5 } \\ \text{ Find the intensity wen D = 2.6 meters} \\ I\text{ = }(k)/(d^2) \\ I\text{ = }(562.5)/((2.6)^2) \\ I\text{ = }(562.5)/(6.76) \\ I\text{ = 83. 2 milliroentgens per our} \end{gathered}`