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Math Help - volume of solids of revolution

  1. #1
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    Exclamation volume of solids of revolution

    A drinking glass has the shape of a truncated cone. IF the internal radii of the base and the top are 3 cm and 4 cm respectively and the depth is 10 cm, find by intergration, its capacity. If the glass is filled with water to a depth of 5 cm, fin the volume of the water.

    I have done question related to intergration but only with the actual formula T_T so i can't work this out.
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  2. #2
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    Hello, chibiusagi!

    A drinking glass has the shape of a truncated cone.
    If the radii of the base and the top are 3 cm and 4 cm respectively
    and the depth is 10 cm, (a) find by intergration, its capacity.

    (b) If the glass is filled with water to a depth of 5 cm,
    find the volume of the water.

    Turn the glass 90; the diagram looks like this:
    Code:
              |
              |           *(10,4)
              |       *   |
              |   *       |
            3 *           |
              |           |
              |           |
              |           |
        - - - * - - - - - * - -
              |          10
    The equation of the line is: . y \:=\:\frac{1}{10}x + 3

    The region bounded by the line, the x-axis, the y-axis, and x=10
    . . is revolved about the x-axis.

    (a) The total volume is: . V \;=\;\pi\int^{10}_0\left(\frac{1}{10}x+3\right)^2\  ,dx

    (b) The volume of the water is: . V \;=\;\pi\int^5_0\left(\frac{1}{10}x+3\right)^2\,dx

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