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10 November, 17:54

The area of circle B is 16 times greater than the area of circle A. Which of the following statements is true? A. The circumference of circle B is 16 times greater than the circumference of circle A. B. The circumference of circle A is 16 times greater than the circumference of circle B. C. The circumference of circle B is 4 times greater than the circumference of circle A. D. The circumference of circle A is 4 times greater than the circumference of circle B.

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Answers (2)
  1. 10 November, 18:03
    0
    Remark

    The general formula for the area of a circle is Area = pi r^2

    The general formula for the circumfrerence of a circle = 2 * pi * r

    Discussion

    You could work with numbers to indicate what the answer might be. You are not asked to prove anything - - just indicate it. Suppose r = 2 for the small circle. It's area is

    A = pi (2) ^2

    A = 4*pi

    Now you want the second circle to be 16 times as big

    16 * 4*pi = pi r1^2 divide both sides by pi

    16*4 = r1^2

    r1^2 = 64

    r1 = 8

    Conclusion

    Radius Circle A = 2

    Radius Circle B = 8

    Solution

    A

    Circumference A = 2 * pi * r = 2 * pi * 2 = 4*pi

    Circumference B = 2 * pi * r1 = 2 * pi * 8 = 16 pi

    Ratio B/A = 16 pi / 4pi = 4

    A is false. It is only 4 times larger.

    B

    The relationship of A to B in circumference is 4 not 16. Answer B is wrong. A and B answers are both wrong.

    C

    The correct answer is C. B is 4 times greater than A.

    D

    D is wrong A is 1/4 the size of B.
  2. 10 November, 18:44
    0
    I took the test and got C) Correct
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