Question

The next hole has a windmill as shown below. Gerald decides that he is never going to be able to time his shot right, so he decides to just randomly swing and hope that the ball makes it past the blades. If the end of each blade is 6 inches and the distance from the center of the fan to the end of a blade is 3 feet, what is the probability of Gerald's shot making it past the windmill? Express your answer as a percent to the nearest tenth.

Answer 1

Answer:

86.7%.

Explanation:

Considering the diagram, the path of the tip of the blades is a circle.

Hence, determine the circumference of the circle.

C = 2πr = 2π * 3 ft = 6π ft.

Then determine how long the blade edges are all together.

6 in * 5 blades = 30 inches

Therefore, to determine the fraction of the circumference of 30 inches, convert circumference to inches

6π ft * (12 in ÷ 1 ft) = 72π in.

Hence, the probability of Gerald’s randomly timed shot hitting a blade of the windmill

=> 30 ÷ 72π

=> 30 ÷ [72 * (22/7)]

= 13.3%.

Finally, the probability of his shot getting past the blades is then 100 – 13.3 = 86.7%.