how to find the ratio of circumference and the ratio of area of two circles?

question 1: if the lengths of the radii of two circles are 1 and 4 respectively, hat is the ratio of their circumference?of their areas?

question 2: the areas of two circles are 9 cm(squared) and 16 cm, squared .what is the ratio of the radii?

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  • 1 decade ago
    Favorite Answer

    RATIO OF THEIR CIRCUMFERENCE :

    Circumference of a circle is " 2 pi r "

    Substitute thr radius in the formula .

    r1 = 1

    r2 = 4

    2 pi r1

    -----------

    2 pi r2

    = > 1 / 4

    RATIO OF THEIR AREAS :

    1/ 16

    2 ) 9 / 16 IS THE RATIO OF THEIR AREAS

    HOPE THIS HELPS................

  • 1 decade ago

    Circumference of Circle = 2 x radii x pi

    Given: 1 and 4

    And since the formula for Circumference does not alter for a Circle, your ratio for Circumference is:

    1 to 4 or 1/4 or 0.25 depending upon what your teacher wants.

    Area of Circle = radius x radius x pi

    Given: 1 and 4:

    It would be 1 x 1 = 1 and 4 x 4 = 16

    Your ratio would be: 1 to 16 or 1/16 or 0.0625

    As for Given: 9 cm squared and 16 cm squared

    You need to square root these which will give you:

    3 and 4.

    Your ratio is: 3 to 4 or 3/4 or 0.75

  • Anonymous
    5 years ago

    This Site Might Help You.

    RE:

    how to find the ratio of circumference and the ratio of area of two circles?

    question 1: if the lengths of the radii of two circles are 1 and 4 respectively, hat is the ratio of their circumference?of their areas?

    question 2: the areas of two circles are 9 cm(squared) and 16 cm, squared .what is the ratio of the radii?

    Source(s): find ratio circumference ratio area circles: https://tr.im/7BjQF
  • 1 decade ago

    Answer 1: Circumference = 2(pi)(r) [r=radius]

    this gives you ratio of circumference as 1:4.

    Area = pi(r^2)

    this gives ratio 1:16.

    Answer 2: 3:4.

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  • 1 decade ago

    Let the radii of both circles be, r and R. where:

    R = 4r (given the 1:4 ratio)

    Now find the circumference of each circle:

    C = 2πR . . . and . . . c = 2πr

    Since R = 4r, substitute it in:

    C = 2πR

    C = 2π(4r)

    C = 8πr

    Now since r/R = 1/4, find the ratio of c/C

    2πr / 8πr = 1/4

    So the circumference is also a 1:4 ratio.

    Now do the same with the Area:

    A = πR² . . . and a = πr²

    A = π(4r)²

    A = 16πr²

    find the ratio a/A:

    πr² / 16πr² = 1/16

    So the ratio of areas are 1:16.

    #2 works this backwards, you've given the areas and need to find the ratio of radii:

    A = πR² . . . and . . .a = πr²

    16 = πR² . . . and . . .9 = πr²

    16/π = R² . . . and . . . 9/π = r²

    4/√π = R . . . and . . . 3/√π = r

    calculate r/R

    (3/√π) / (4/√π)

    (3/√π) * (√π /4)

    3/4

    The ratio is 3:4.

  • Anonymous
    5 years ago

    A1/A2 = 6(pi)m^2 / 150(pi)m^2 = 1/25 A1/A2 = 1/25 = 1/5^2 since Area is proportional to the radius and likewise, Circumference is proportional to the radius of the circle. If A1?A2 = 1/25 (=1/5^2) then So, c1/c2 = 1/5 <= ANS

  • 7 years ago

    Find the ratio of the circumferences of two circles, radii 10cm and 15cm.

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