# Volume of Revolution

• Apr 18th 2009, 07:49 AM
Hakhengkim
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]
• Apr 18th 2009, 07:59 AM
skeeter
Quote:

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]

$V = \pi \int_0^1 (\sqrt{x})^2 \, dx$
• Apr 18th 2009, 08:28 AM
Hakhengkim
Quote:

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

Thanks :D
• Apr 18th 2009, 09:05 AM
Twig
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.