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Math Help - volume and algebra problems

  1. #1
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    volume and algebra problems

    The radius of a right circular cone is doubled and its height is tripled to form a new right circular cone. What is the ratio of the volume of the original cone to the new one?
    Seems to be a 1:12 ratio but I always come up with 1:6??

    The variables a, b, and c are all integers and a + b + c = 50. If a < 0, and 0 < b < 30, then the minimum possible value for c is 22. Why?
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by sarahh View Post
    The variables a, b, and c are all integers and a + b + c = 50. If a < 0, and 0 < b < 30, then the minimum possible value for c is 22. Why?
    The maximum value for a is -1 and for b is 29. When you add them you get 28, and you need another 22 to make 50.

    (I'll look up the formula for a cone just now, i forgot it again )
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by sarahh View Post
    The radius of a right circular cone is doubled and its height is tripled to form a new right circular cone. What is the ratio of the volume of the original cone to the new one?
    Seems to be a 1:12 ratio but I always come up with 1:6??
    Right the first cone's volume is \frac{1}{3} \pi r^2 h

    For the second cone we have: \frac{1}{3} \pi (2r)^2 (3h)

    \frac{1}{3} \pi r^2 h \ \ : \ \ \frac{1}{3} \pi (2r)^2 (3h)

    r^2 h \ \ : \ \ 4r^2 (3h)

    1 : 12
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    Thanks for your help jandvl--those were driving me crazy!
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by sarahh View Post
    Thanks for your help jandvl--those were driving me crazy!
    You're welcome
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