CPM Homework Help : AC Problem 2-59

A dart hits each dartboard below at random. What is the probability that the dart will land in the darkly shaded area? Homework Help ✎

Step 1 (a):

First find the total area of the dartboard. A = r²?

16π

Step 2(a):

Subtract the area of the lighter, smaller circle from the total area of the whole circle.

16π − 4π = 12π

Step 3(a):

Divide the difference between the areas of the dartboardand the small circle by the area of the dartboard.

$\frac{12\pi}{16\pi}$

Answer (a):

$\text{The probability is }\frac{3}{4}.$

Hint (b):

Use the same method from part (a).