I've been trying to figure out why you can't use the average value of a function to determine the volume of a solid of revolution.(adsbygoogle = window.adsbygoogle || []).push({});

As an example:

Trying to find the volume of a solid of revolution on y=√x from 0 to 1 around the x-axis.

The definite integral is 2/3, which divided by one is still 2/3 so it is the average value.

Then I tried to use turn this into a problem of finding the volume of a solid of revolution around the y=2/3. a radius of 2/3 from 0 to 1. I Since the sides were a straight line I tried to solve for the volume of a cylinder with radius 2/3 and height.

But this didn't work. I've been wracking my brain for like half an hour trying to figure out why but I've got nothing. Can anyone explain to me why this doesn't work?

Thanks in advance.

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# I Confusion on the Volumes of Solids of Revolution

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