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Math Help - Integral Calculus

  1. #1
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    Exclamation Integral Calculus

    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 integration, its capacity. If the glass is filled with water to a depth of 5 cm, find the volume of the water.

    Could someone please show me how to do this question?
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  2. #2
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    Hello xwrathbringerx
    Quote Originally Posted by xwrathbringerx View Post
    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 integration, its capacity. If the glass is filled with water to a depth of 5 cm, find the volume of the water.

    Could someone please show me how to do this question?
    Imagine the glass to be the solid formed when the line joining (3,0) to (4,10) is rotated about the y-axis.

    The equation of this line is y = 10x-30, and the volume of revolution about the y-axis is

    \int_0^{10}\pi x^2dy

    Can you continue?

    Grandad
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