Question

A dart hits the small circular target shown below at a random point. Find the probability that the dart lands in the shaded circular region. The radius of the target is 8 cm, and the radius of the shaded region is 3 cm.

Use the value 3.14 for π. Round your answer to the nearest hundredth.

Answer 1

Answer: The probability is P = 0.14

Explanation:

We know that the dart will land on the larger circle, then we have a 100% of probability that the dart will land on the larger circle.

Then the probability of the dart landing on the smaller circle will be equal to the quotient between the areas of the smaller circle and the larger circle.

The area of a circle of radius R is:

A = 3.14*R^2

Then the area of the larger circle is:

A = 3.14*(8cm)^2 = 200.96 cm^2

And the area of the smallest circle is:

a = 3.14*(3cm)^2 = 28.26 cm^2

Then the probability of the dart landing on the shaded region is:

P = (28.26 cm^2)/(200.96 cm^2) = 0.14