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Math Help - Volume of Revolution

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    Volume of Revolution

    Find the volume of revolution when the graph of y=√ x is rotated about the x axis, in the interval [0,1]
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    Quote Originally Posted by Hakhengkim View Post
    Find the volume of revolution when the graph of y=√ x is rotated about the x axis, in the interval [0,1]
    V = \pi \int_0^1 (\sqrt{x})^2 \, dx
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    Quote Originally Posted by skeeter View Post
    V = \pi \int_0^1 (\sqrt{x})^2 \, dx
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    Senior Member Twig's Avatar
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    Itīs worth pointing out that the volume of a thin slice is  y^{2}\cdot \pi \cdot \Delta x
    Since  y = \sqrt{x} \Rightarrow y^{2} = (\sqrt{x})^{2}
    You will get the volume as an integral when you let  \Delta x approach zero.

    So the formula  \pi \int_{a}^{b} \, y^{2} \, dx comes from the volume of a thin slice.
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