Cone's volume, not seeing a step posted elsewhere

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SUMMARY

The discussion centers on the calculation of a cone's volume using integral calculus. Specifically, the volume is derived by slicing the cone into infinitesimally thin discs at height x, where the radius of each disc is determined by the ratio x/h multiplied by the base radius (r). The volume of each disc is calculated as π times the square of the radius times the thickness dx. This method confirms the correctness of the integral approach to finding the volume of a cone.

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Damascus Road
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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!
 
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Damascus Road said:
I'm not sure why it's squared, or why the x is there.

Hi Damascus Road! :smile:

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.
 

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