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Find the volume of the solid generated by revolving the region bounded by y={\sqrt  {x}}, the x-axis and the line x=4 around the x-axis.

This is pretty straightforward. We will integrate x on the interval [0,4]. There is only one function so we do not need to subtract out any hole in the middle.

V=\pi \int _{{0}}^{{4}}({\sqrt  {x}})^{2}\,dx=\pi \left[{\frac  {1}{2}}x^{2}\right]_{{0}}^{{4}}=8\pi

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