A rectangular dartboard measures 10 units by 20 units. A circular target area with a radius of 5 units is painted on the dartboard. If a dart is thrown and lands randomly on the board, what is the probability that it lands within the circular target area?

Question

*
π/16
π/8
π/4
π/2

Answer 1

The area of the circular target area is πr^2 = π(5)^2 = 25π square units.

The area of the rectangle containing the target area is 10 * 20 = 200 square units.

Therefore, the probability that the dart lands within the circular target area is the ratio of the area of the circular target area to the total area of the rectangle, which is:

(25π) / 200 = π / 8

Therefore, the probability that the dart lands within the circular target area is π/8.