Hello, this is my first time posting on physics forums, so if I do something wrong, please bear with me :)(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to derive the formula for the lateral surface area of a cone by cutting the cone into disks with differential 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. And using dS instead of dH allowed me to find the correct formula for the lateral area of the cone!

HOWEVER, using dS instead of dH contradicts with the same method for finding the volume of the cone. I basically used the method shown in another person's video () to find the volume of the cone, but that person assumed that the height of each disk is dH, not dS.

So is the height of each disk dS or dH? If it is dS, then I understand how to get the formula for the lateral surface area of the cone, but not the volume. But if it is dH, then I understand how to get the formula for the volume of the cone, not the surface area. Can anyone clear up my confusion? I know that there are other methods to find the surface area/volume, but I just want to know why there is a contradiction between the dH/dS thing. Thanks! Any help is appreciated! :)

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deriving the volume and surface area of a cone

Loading...

Similar Threads - Deriving volume surface | Date |
---|---|

I Derivation for the volume of a cone | Dec 23, 2016 |

I Deriving the volume of a sphere using semi-circles | Oct 11, 2016 |

Maximize volume of a box | Apr 8, 2015 |

Attempt at Deriving the Volume of a Cone | May 28, 2011 |

Derivative of the Volume of a Cone | Nov 25, 2007 |

**Physics Forums - The Fusion of Science and Community**