Volume of Revolution

**Hakhengkim** · April 18th 2009, 07:49 AM

Find the volume of revolution when the graph of y=√ x is rotated about the x axis, in the interval [0,1]

**skeeter** · April 18th 2009, 07:59 AM

Originally Posted by Hakhengkim

Find the volume of revolution when the graph of y=√ x is rotated about the x axis, in the interval [0,1]

$V = \pi \int_0^1 (\sqrt{x})^2 \, dx$

**Hakhengkim** · April 18th 2009, 08:28 AM

Originally Posted by skeeter

$V = \pi \int_0^1 (\sqrt{x})^2 \, dx$

Thanks

**Twig** · April 18th 2009, 09:05 AM

It´s 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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