Hint

Property When finding the ratio of the areas of two circles, leave the areas in terms of $\pi$ to make simplification easier.

Explanation Think of $\pi$ as a tagalong in your calculations. By keeping it in your numerator and denominator, you can cancel it out instantly, just like a common factor. This trick avoids messy decimals and simplifies your fraction crunching life. Work smarter, not harder, and let pi cancel itself out of the equation for a clean finish!

Examples A target has a 15 inch radius outer circle and a 5 inch radius inner circle. The probability of hitting the inner circle is $$ \operatorname{P}(\text{inner}) = \frac{\pi(5)^2}{\pi(15)^2} = \frac{25\pi}{225\pi} = \frac{1}{9} $$. A school zone has a 3 mile radius. Students within a 1 mile radius can walk. The probability a student is a walker is $$ \operatorname{P}(\text{walk}) = \frac{\pi(1)^2}{\pi(3)^2} = \frac{1\pi}{9\pi} = \frac{1}{9} $$.