Answer:
The probability that the dart lands inside the square but not on the circular dartboard is 0.215
Step-by-step explanation:
* Lets explain how to solve the problem
- The dartboard consists of a circle inscribed in a square
∵ The circle is inscribed in the square
∴ The four sides of the square are tangents to the circle
∴ The diameter of the circle = the side of the square because the
sides of the squares touch the circle at the end points of its
diameter
∵ The area of the square = 64 inches²
∵ The area of the square = (side)²
∴ 64 = (side)² ⇒ take √ for both sides
∴ side = √64 = 8 inches
∴ The diameter of the circle = 8 inches
∵ The radius = diameter ÷ 2
∴ The radius = 8 ÷ 2 = 4 inches
∵ The area of the circle = πr²
∵ π = 3.14
∴ The area of the circle = 3.14(4)² = 50.24 inches
- Lets calculate the area of the part inside the square not in the circle
∵ The area of the square = 64 inches²
∵ The area of the circle = 50.24 inches²
∴ The area in the square not in the circle = 64 - 50.24 = 13.76 inches²
- The probability = the event occurs/total events
∵ P(inside the square not the circle) = area in the square not in the
circle ÷ area of the square
∴ P(inside the square not the circle) = 13.76/64 = 0.215
* The probability that the dart lands inside the square but not on the
circular dartboard is 0.215
