algebra

The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 50π cubic inches when the radius is 5 inches and the height is 6 inches, find the volume of a cone when the radius is 4 inches and the height is 3 inches

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  1. 50π * (4/5)^2 * (3/6)

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  2. So would it be 16

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  3. You should know that
    volume of cone = (1/3) π r^2 h
    if not, then ....

    V = k r^2 h
    when V = 50π, r = 5, and h = 6
    50π = k(25)(6)
    k = 50π/(150) = π/3 or (1/3)π , how about that?

    V = (1/3)π (4^2)(3) cubic inches = same answer at R_scott,
    and certainly not 16

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    Reiny
  4. So would it be 16 π ? Ugh lol no matter what I do I keep getting 16. Thank you guys for your help trying to explain to me :)

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  5. You are told that
    v = k r^2 h
    That means that V/(r^2 h) = k, a constant, which does not change. So now you know you are looking for v such that

    v/(4^2 * 3) = 50π/(5^2 * 6)
    v/48 = 50π/150 = π/3
    v = 48π/3 = 16π

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    oobleck

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