Question #151633
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.
1
Expert's answer
2020-12-17T18:59:11-0500

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 = area of shaded regiontotal area=28.2749=\dfrac{\textsf{area of shaded region}}{\textsf{total area}} = \dfrac{28.27}{49} = 0.577


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