- #1
dtseng96
- 13
- 0
Hello, I have actually asked a similar question before, but I just realized something and I want to edit the question now:
I am trying to derive the formula for the lateral surface area of a cone by cutting the cone into disks with infinitesimal height, and then adding up the lateral areas of all of the disks/cylinders to find the lateral area of the cone. (Similar to using the volume of revolution, but just taking the surface area). I assumed that the heights of each of the disk was dH, where H = the height of the cone. However, using that method, I got pi*radius*height instead of pi*radius*(slant height).
On another thread in physics forum (https://www.physicsforums.com/showthread.php?t=354134) , a person used a similar method as I did, and someone replied saying that the height of each disk is dS, where S = the slant height of the cone, not dH, where H = the height of the cone. This seems to work. However, it doesn't make sense to me, because it seems like the height of each disk should be dH, not dS. I tried to show my argument/confusion in this picture:
http://dl.dropbox.com/u/29312856/Cone.jpg
P.S. I basically used the method shown in another person's video () to find the volume of the cone, and that person assumed that the height of each disk is dH, not dS, and in that case, dH worked. :O
Can anyone tell me why the height of each cylinder is dS, not dH? Or can anyone tell me what I am doing wrong? Thanks in advance! It's been bothering me for days... :(
I am trying to derive the formula for the lateral surface area of a cone by cutting the cone into disks with infinitesimal height, and then adding up the lateral areas of all of the disks/cylinders to find the lateral area of the cone. (Similar to using the volume of revolution, but just taking the surface area). I assumed that the heights of each of the disk was dH, where H = the height of the cone. However, using that method, I got pi*radius*height instead of pi*radius*(slant height).
On another thread in physics forum (https://www.physicsforums.com/showthread.php?t=354134) , a person used a similar method as I did, and someone replied saying that the height of each disk is dS, where S = the slant height of the cone, not dH, where H = the height of the cone. This seems to work. However, it doesn't make sense to me, because it seems like the height of each disk should be dH, not dS. I tried to show my argument/confusion in this picture:
http://dl.dropbox.com/u/29312856/Cone.jpg
P.S. I basically used the method shown in another person's video () to find the volume of the cone, and that person assumed that the height of each disk is dH, not dS, and in that case, dH worked. :O
Can anyone tell me why the height of each cylinder is dS, not dH? Or can anyone tell me what I am doing wrong? Thanks in advance! It's been bothering me for days... :(
Last edited by a moderator: