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Volume of apple juice

  1. Mar 30, 2014 #1
    A cylindrical container of height 1 m and diameter 0.5 m is partially filled with apple juice. When the container is lying on its side, the juice level at the deepest point is 37.5 cm (three eighths of a meter from the bottom of the cylinder is full). What is the liquid level after the container is raised up?

    What I thought of doing is that I found the intersection of the radius with the point where the juice is at its maximum. By using Pythagoras and trig functions, I could find the angle from which the radius goes from the center to the top of the juice.

    Now, I use the shell method, but instead of using 2pi, I used 4.1888.

    Integral of 4.188*y*(0.25) dy
    Then I added the triangular pyramid that was chopped off.

    Is my method correct? Could you please tell me how you would do this.
     
  2. jcsd
  3. Mar 30, 2014 #2

    Simon Bridge

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    What triangular pyramid? Sounds confused.
    Why not use the slice method ... sketch the cylinder end-on and divide the filled section into horizontal slices.
     
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