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Thread: 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 $\displaystyle (3,0)$ to $\displaystyle (4,10)$ is rotated about the $\displaystyle y$-axis.

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

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

    Can you continue?

    Grandad
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