The circumference of a circle is 28. Contained in that circle is a smaller circle with area 36π. A point is selected at random from inside t

Question

The circumference of a circle is 28. Contained in that circle is a smaller circle with area 36π. A point is selected at random from inside the large circle. What is the probability the point also lies in the smaller circle?

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Delwyn 6 months 2021-07-30T12:35:31+00:00 1 Answers 1 views 0

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    2021-07-30T12:37:19+00:00

    Answer:

    Pr = \frac{9}{49}

    Step-by-step explanation:

    Given

    d = 28 — big circle

    A_2 = 36 \pi — area of small circle

    Required

    Probability that a point selected lands on the small circle

    Calculate the area of the big circle using;

    A_1 = \pi r^2

    Where

    r = d/2

    So, we have:

    r = 28/2 = 14

    This gives:

    A_1 = \pi * 14^2

    A_1 = \pi * 196

    A_1 = 196\pi

    The probability that a point selected lands on the small circle is calculated by dividing the area of the small cicle by the big circle

    This gives:

    Pr = \frac{36\pi}{196\pi}

    Pr = \frac{36}{196}

    Simplify

    Pr = \frac{9}{49}

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