Answer
$45$ foot-candles
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the intensity of the light be $I$.
and the distance from the source be $D$.
$\Rightarrow I=\frac{k}{D^2}$ ...... (1)
Step 2:- Substitute the first set of values into equation (1) to find the value of $k$.
The given values are $I=20$ foot-candles and $D=15$ feet.
Substitute into equation (1).
$\Rightarrow 20=\frac{k}{15^2}$
$\Rightarrow 20=\frac{k}{225}$
Multiply both sides by $225$.
$\Rightarrow 225\cdot 20=225\cdot \frac{k}{225}$
Simplify.
$\Rightarrow 4500=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=4500$ into equation (1).
$\Rightarrow I=\frac{4500}{D^2}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $D=10$ feet into equation (2).
$\Rightarrow I=\frac{4500}{10^2}$
Simplify.
$\Rightarrow I=\frac{4500}{100}$
$\Rightarrow I=45$
Hence, the intensity of the light is $45$ foot-candles.
