The circle has an area of 314 square centimeters, and the square inside the circle has a side length of 2 centimeters. What is the probability that a point chosen at random is in the blue region?
Answers
Step-by-step explanation:
Answer:
77.5%
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the radius of the circle
The area of the circle is
we have
assume
substitute and solve for r
step 2
Find the area of the square outside the circle
The length side of the square is the diameter of the circle
step 3
Determine the area of the blue region
The area of the blue region is the area of circle minus the area of the square inside the circle
step 4
The probability that a point chosen at random is in the blue region is equal to divide the area of the blue region by the total area of the outside square
310/400
simplify
31/40=0.775
Convert to percentage
0.775*100=77.5%...
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