The sum of the two areas of two circles is the 80x square meters. Find the length of a radius of each circle of them is twice as long as the

Question

The sum of the two areas of two circles is the 80x square meters. Find the length of a radius of each circle of them is twice as long as the other. What is the radius of the larger circle?

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Bơ 3 years 2021-08-22T16:14:29+00:00 1 Answers 66 views 0

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  1. Calantha
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    2021-08-22T16:15:40+00:00
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    Answer:

    r = 4m — small circle

    R =8m — big circle

    Step-by-step explanation:

    Given

    Area = 80\pi\ m^2 — sum of areas

    R = 2r

    Required

    The radius of the larger circle

    Area is calculated as;

    Area = \pi r^2

    For the smaller circle, we have:

    A_1 = \pi r^2

    For the big, we have

    A_2 = \pi R^2

    The sum of both is:

    Area = A_1 + A_2

    Area = \pi r^2 + \pi R^2

    Substitute: R = 2r

    Area = \pi r^2 + \pi (2r)^2

    Area = \pi r^2 + \pi *4r^2

    Substitute Area = 80\pi\ m^2

    80\pi = \pi r^2 + \pi *4r^2

    Factorize

    80\pi = \pi[ r^2 + 4r^2]

    80\pi = \pi[ 5r^2]

    Divide both sides by \pi

    80 = 5r^2

    Divide both sides by 5

    16 = r^2

    Take square roots of both sides

    4 = r

    r = 4m

    The radius of the larger circle is:

    R = 2r

    R =2 * 4

    R =8m

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