Volume of solid of revolution

**roze** · April 9th 2010, 07:49 AM

can u plzz help me with this math..??

find the volume of the solid that results when the region enclosed by y=root x,y=o and x=9 is resolved about the line x=9.

plzz help mee.....

**macosxnerd101** · April 9th 2010, 05:08 PM

The best thing you can do here is to graph your equations. When you revolve them around the line x = 9, you get an ellipsoid. So now what you have to do is ask yourself, what would a slice of this ellipsoid look like? It would be an elliptical cylinder.

So if you use the disk method, you want to find the volume of the slice, which is the pi * Area * width. So we integrate:
$<br /> \pi * \displaystyle\int^b_a Area\,dx<br />$

**eddie2042** · April 9th 2010, 10:57 PM

Originally Posted by roze

can u plzz help me with this math..??

find the volume of the solid that results when the region enclosed by y=root x,y=o and x=9 is resolved about the line x=9.

plzz help mee.....

Easy. Using the method of cylindrical shells:

$V = 2\pi\int_0^9(9-x)\cdot(\sqrt{x})dx$
$V = 2\pi\int_0^99x^\frac{1}{2} - x^\frac{3}{2} dx$
$V = 2\pi\left[6x^\frac{3}{2} - \frac{2x^\frac{5}{2}}{5}\right]_0^9$
$V = \frac{648\pi}{5}$

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