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Math Help - Work: Spherical Problem

  1. #1
    Member RedBarchetta's Avatar
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    Work: Spherical Problem

    A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g and 3.14 for . Round your answer to three significant digits.) W=_________

    r=3
    h=1


    To set up this problem, I tried by taking the area of one slice of water to be pi r^2. Then multiply this by 1000 kg/m^3 to get the volume of one slice.

    Now I want R as a function of, lets say y. We know the area of a circle is r^2+y^2=3^2. So r=sqrt(9-y^2). Also, the distance for any slice from the top is 7-y.

    After this I tried integrating from zero to six of the function 1000*pi*(9-y^2)*(7-y). This came out to be 36000pi. Which is 113097.3355 Joules.

    Apparently, that is wrong. What am I doing wrong?

    Thank you!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by RedBarchetta View Post
    A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g and 3.14 for . Round your answer to three significant digits.) W=_________

    r=3
    h=1


    To set up this problem, I tried by taking the area of one slice of water to be pi r^2. Then multiply this by 1000 kg/m^3 to get the volume of one slice.

    Now I want R as a function of, lets say y. We know the area of a circle is r^2+y^2=3^2. So r=sqrt(9-y^2). Also, the distance for any slice from the top is 7-y.

    After this I tried integrating from zero to six of the function 1000*pi*(9-y^2)*(7-y). This came out to be 36000pi. Which is 113097.3355 Joules.

    Apparently, that is wrong. What am I doing wrong?

    Thank you!
    I think your first mistake was trying to find the volume of a two-dimensional cross-section
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  3. #3
    Member RedBarchetta's Avatar
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    Ah, I think I know what I missed. Delta Y.

    Each slice is a cylinder, with the volume= 1000*pi*r^2*delta y.
    Last edited by RedBarchetta; May 11th 2008 at 10:08 PM.
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