# Math Help - Volume of Revolution

1. ## 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]

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

3. Originally Posted by skeeter
$V = \pi \int_0^1 (\sqrt{x})^2 \, dx$
Thanks

4. 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.