Help with integrating the volume of cone while keeping the cone the right way up.

galen burnett

New member
Joined
Oct 27, 2021
Messages
5
I was watching this video on how to integrate the volume of a cone. I understand that he turns the cone upside-down to make the working easier. However, to fully understand this part, where he turns it upside-down, I wanted to try and complete the sequence by keeping the cone the right way up. I didn't succeed because the formula I got for the volume, which is the last line of maths in the document I attached to this post, doesn't give the right figures. But I can't see where I went wrong; could anyone show me where my working went wrong please?

Also I don't quite get how you are allowed to turn the cone upside-down and for it still to work, if anyone could explain that in some detail that would be great.
 

Attachments

  • cone q pdf.pdf
    33.9 KB · Views: 6

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
7,770
I don't see anywhere in what you have posted that gives the actual original cone!
 

blamocur

Full Member
Joined
Oct 30, 2021
Messages
575
I was watching this video on how to integrate the volume of a cone. I understand that he turns the cone upside-down to make the working easier. However, to fully understand this part, where he turns it upside-down, I wanted to try and complete the sequence by keeping the cone the right way up. I didn't succeed because the formula I got for the volume, which is the last line of maths in the document I attached to this post, doesn't give the right figures. But I can't see where I went wrong; could anyone show me where my working went wrong please?
Also I don't quite get how you are allowed to turn the cone upside-down and for it still to work, if anyone could explain that in some detail that would be great.
I believe there is an error in the second line of formulae in your attachment. In fact, you can tell it can't be right if you try assigning units to different parts of the equations; e.g. r/R is "unitless", but H is not
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
11,474
Do you really think that the volume of a given cone depends on its orientation? The volume will be the same if it is upside down, rightsize up, rotated 34 degrees clockwise, etc.
 
Top