Cone's volume, not seeing a step posted elsewhere

[Damascus Road]

Hey all,

can you check out this site

http://www.mathisfunforum.com/viewtopic.php?pid=49738

In the very first line of the integral, I'm not sure why it's squared, or why the x is there. Can someone explain this?
Clearly, its correct because the correct answer is derived lol.

Thanks!

 

[tiny-tim]

I'm not sure why it's squared, or why the x is there.

Hi Damascus Road!

The cone is sliced into discs of thickness dx at height x.

So the radius of each disc is x/h times the base radius (r),

and the volume of the disc is that squared times π times dx.