MathematicsIf the area of a circle increases from 9π   to 16π,   then what will be the ratio of the circumference of the first circle to the second circle?

If the area of a circle increases from 9π   to 16π,   then what will be the ratio of the circumference of the first circle to the second circle?


  1. A
    3: 4
  2. B
    4: 3
  3. C
    2: 3
  4. D
    3: 2 

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    Solution:

    Given, the increment in the area of a circle is from 9π   to 16π  .
    We have to find the ratio of the circumference of the first circle to the second circle.
    We know that area of the circle is A=π r 2  .
    Let for circle 1, the area of the circle is A 1 =π r 1 2   and for circle 2, the area of the circle is A 2 =π r 2 2  .
    We get,
    A 1 =π r 1 2 9π=π r 1 2 9= r 1 2 r 1 =3  
    Also,
    A 2 =π r 2 2 16π=π r 2 2 16= r 2 2 r 2 =4  
    Now, the circumference of a circle is given by C=2πr  .
    Circumference of circle 1 is C 1 =2π r 1  .
    C 1 =2π r 1 C 1 =2π×3 C 1 =6π  
    Also,
    C 2 =2π r 2 C 2 =2π×4 C 2 =8π  
    Now, the ratio of the circumference of the first circle to the second circle is given by,
    C 1 : C 2 6π:8π 3:4  
    Therefore, the ratio of the circumference of the first circle to the second circle is 3: 4.
    Hence, the correct option is 1.
     
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