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Math Help - "Star Problems" Volume as a function of height

  1. #1
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    Exclamation "Star Problems" Volume as a function of height

    Hello Everyone,

    I need help on problems like this one:

    A water tank is the shape of an inverted cone which has a height of 120 meters and a diameter at the top of 60 meters. Water starts flowing out of the tank at a rate of 5 cubic meters per second.
    Find the volume of the water, V, as a function of water height, H.
    Find H as a function of time, T, since the water started flowing from a full tank.

    If you know how to do this please reply
    Thanks!
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  2. #2
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    Quote Originally Posted by wildcurls View Post
    Hello Everyone,

    I need help on problems like this one:

    A water tank is the shape of an inverted cone which has a height of 120 meters and a diameter at the top of 60 meters. Water starts flowing out of the tank at a rate of 5 cubic meters per second.
    Find the volume of the water, V, as a function of water height, H.
    Find H as a function of time, T, since the water started flowing from a full tank.

    If you know how to do this please reply
    Thanks!
    see the following thread ...

    http://www.mathhelpforum.com/math-he...ted-rates.html
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  3. #3
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    Thanks for replying!
    Unfortunatly that didn't really help me much. I don't know what derivative of w/r means or the If some one could explain these it might help me more. My pre-cal teacher is really frustrating, he didn't explain these problems just handed them out. Can someone explain this to me in pre-cal language?
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  4. #4
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    Quote Originally Posted by wildcurls View Post
    Thanks for replying!
    Unfortunatly that didn't really help me much. I don't know what derivative of w/r means or the If some one could explain these it might help me more. My pre-cal teacher is really frustrating, he didn't explain these problems just handed them out. Can someone explain this to me in pre-cal language?
    Volume of the cone V = \frac{1}{3}\pi{r^2h}

    If H is the height of the cone and R is the radius of the base, then \frac{H}{R} = \frac{h}{r}

    r = \frac{hR}{H}

    Substitute this value in V to get V in terms of h.
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  5. #5
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    A water tank is the shape of an inverted cone which has a height of 120 meters and a diameter at the top of 60 meters. Water starts flowing out of the tank at a rate of 5 cubic meters per second.
    Find the volume of the water, V, as a function of water height, H.
    Find H as a function of time, T, since the water started flowing from a full tank.
    the water in the tank forms a conical shape similar to the entire cone.

    let r = radius of the water surface

    h = height of the water surface

     <br />
\frac{r}{h} = \frac{30}{120} = \frac{1}{4}<br />

    so, 4r = h or r = \frac{h}{4}

    let V = volume of water in the tank

     <br />
V = \frac{\pi}{3} r^2 h<br />

    substitute \frac{h}{4} for r in the volume equation

     <br />
V = \frac{\pi}{3} \left(\frac{h}{4}\right)^2 h<br />

     <br />
V = \frac{\pi}{48} h^3<br />

    since V = 5t ...

     <br />
5t = \frac{\pi}{48} h^3<br />

    to get h as a function of time, solve the last equation for h.
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  6. #6
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    Thank you!!!
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