Answer
$90\; milliroentgens\; per \; hour $.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the intensity of radiation be $I$
and the distance from machine be $D$.
Because $I$ varies inversely as $D^2$ we have:
$\Rightarrow I=\frac{k}{D^2}$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $D=3\; meters$
and $I=62.5\; milliroentgens\; per \; hour$.
Substitute into the equation (1).
$\Rightarrow 62.5=\frac{k}{3^2}$
$\Rightarrow 62.5=\frac{k}{9}$
Multiply both sides by $9$.
$\Rightarrow 9\cdot 62.5=9\cdot \frac{k}{9}$
Simplify.
$\Rightarrow 562.5=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=562.5$ into the equation (1).
$\Rightarrow I=\frac{562.5}{D^2}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $D=2.5\;meters$ into the equation (2).
$\Rightarrow I=\frac{562.5}{(2.5)^2}$
Simplify.
$\Rightarrow I=90$
Hence, the intensity is $90\; milliroentgens\; per \; hour $.
