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Math Help - An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing o

  1. #1
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    An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing o

    An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing out of the vertex of the container at a rate of 35 \pi in^3/sec , how fast is the depth of the water dropping when the height is 5in?
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    Quote Originally Posted by yoman360 View Post
    An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing out of the vertex of the container at a rate of 35 \pi in^3/sec , how fast is the depth of the water dropping when the height is 5in?
    Volume of the cone V = 1/3*π*r^2*h.....(1)
    You want to find dh/dt. So you have to find r in terms of h.
    r and h are proportional tp R and H, where R = 21" and H = 15".
    So R/H = r/h.
    So r = (R/H)*h.
    Substitute this value in the eq.(1) and find dV/dt.
    dV/dt is given. Find dh/dt.
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Volume of the cone V = 1/3*π*r^2*h.....(1)
    You want to find dh/dt. So you have to find r in terms of h.
    r and h are proportional tp R and H, where R = 21" and H = 15".
    So R/H = r/h.
    So r = (R/H)*h.
    Substitute this value in the eq.(1) and find dV/dt.
    dV/dt is given. Find dh/dt.
    I followed your steps and this is what I get:
    r=\frac{21}{15} h

    v=\frac{1}{3}\pi(\frac{21}{15}h)^2*h

    simplify so v=\pi\frac{49}{75}h^3

    dv/dt=\pi\frac{49}{25}h^2* dh/dt

    plug in h and dv/dt

    35\pi=\pi\frac{49}{25}(15)^2* dh/dt

    solve for dh/dt i get

    dh/dt=\frac{5}{63} in/sec

    the problem is that the answer key says the answer is \frac{5}{7} in/sec

    what did i do incorrectly?
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  4. #4
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    Quote Originally Posted by yoman360 View Post
    I followed your steps and this is what I get:

    plug in h dv/dt=\pi\frac{49}{25}(15)^2* dh/dt
    Never mind. h=5 and H= 15
    I figured it out I was suppose to plug in 5 here instead if 15 then solving for dh/dt i got 5/7 in/sec

    Thanks for the help
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