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 probabili

Question

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?

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Melanie 1 month 2021-08-21T14:25:35+00:00 1 Answer 0 views 0

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    2021-08-21T14:26:46+00:00

    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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