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anonymous

  • one year ago

*MEDAL WILL BE AWARDED* The radii of two circles are in the ratio of 3 to 1. Find the area of the smaller circle if the area of the larger circle is 27pi sq. in. a) 9 b) 6 c) 3

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  1. anonymous
    • one year ago
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    ooh a medal!

  2. anonymous
    • one year ago
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    Yes a medal

  3. anonymous
    • one year ago
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    Are you jumping around or what? It's like you're answering like 10 questions at a time! Lol! :D

  4. anonymous
    • one year ago
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    i am trying to get all the medals i can so i can trade in my bike for a kia sedona

  5. anonymous
    • one year ago
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    Cool

  6. anonymous
    • one year ago
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    the area comes with the square of the radius

  7. anonymous
    • one year ago
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    so it the ratio of the radius is 3 : 1 the ratio of the area is \(3^2:1\) i.e. \(9:1\)

  8. anonymous
    • one year ago
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    Oh. I thought you were supposed to divide 27 by 3 and get 9?

  9. anonymous
    • one year ago
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    no

  10. anonymous
    • one year ago
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    suppose one circle has radius 1, it has area \(\pi\) and another one has radius 3, it has area \(9\pi\) i.e. its area is 9 times as large, not 3 times

  11. anonymous
    • one year ago
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    if the larger circle has area 27, then the smaller one has areas one-ninth as large \[\frac{27}{9}\]

  12. anonymous
    • one year ago
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    So the area is 3?

  13. anonymous
    • one year ago
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    smaller has area 3 yes

  14. anonymous
    • one year ago
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    Btw the answers are a) 9pi b) 6pi c) 3pi

  15. anonymous
    • one year ago
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    so is it A?`

  16. anonymous
    • one year ago
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    no

  17. anonymous
    • one year ago
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    c?

  18. anonymous
    • one year ago
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    yes

  19. anonymous
    • one year ago
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    you want to take half a minute i can explain easy

  20. anonymous
    • one year ago
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    Okay thanks so much! That would be a big help

  21. anonymous
    • one year ago
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    lets forget about a circle just use a square the area of a square with side \(a\) is \(a^2\) like if the side is 4 the area is 16

  22. anonymous
    • one year ago
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    now suppose you have another square whose sides is 3 times as large, so sides is12 the area of that square is \(12^2=144\)

  23. anonymous
    • one year ago
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    And the little one is 48

  24. anonymous
    • one year ago
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    the ratio of the sides is \(3:1\) but the ratio of the areas is \(144:16=9:1\)

  25. anonymous
    • one year ago
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    in other words, the ratio of the areas is the square of the ratio of the sides

  26. anonymous
    • one year ago
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    supposed you had one square with side 1, its area is 1 another has side 3, its area is 9 ratio of sides 3:1 ratio of areas 9:1

  27. anonymous
    • one year ago
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    same with the circle ratio of radii 3:1 ratio of area 9:1

  28. anonymous
    • one year ago
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    So sides and areas will always be different? I think that's where I had went wrong

  29. anonymous
    • one year ago
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    yes the ratio of the area is the SQUARE of the ratio of the sides this should not be too surprising because the side is measured in length (one dimensional unit like feet or meters) and the area is measured in SQUARE units, like square feet or square meters

  30. anonymous
    • one year ago
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    so if the ratio of the sides is say \(5:2\) then the ratio of the areas is \(25:4\)

  31. anonymous
    • one year ago
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    Oh wow that makes so much more sense now

  32. anonymous
    • one year ago
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    glad to help you got another one we can try ?

  33. anonymous
    • one year ago
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    I was just about to ask you too Lol!

  34. anonymous
    • one year ago
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    Yes of course!

  35. anonymous
    • one year ago
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    go ahead i will take a look, but first give me your answer

  36. anonymous
    • one year ago
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    Alright I sure will

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