Answer to Question #151633 in Geometry for roberto

Question

A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is 7in, and the radius of the shaded region is 3in.

Answer 1

radius of the shaded circular region (r) = 3 inches

length of the square shaped dartboard (l) = 7 inches

Area of the shaded circular region on the dartboard = πr² = π × 3² = 28.27 in²

Total area of the square shaped dartboard = l² = 7² = 49 in²

The probability of it landing on the shaded circular region = $\dfrac{\textsf{area of shaded region}}{\textsf{total area}} = \dfrac{28.27}{49} =$ 0.577