The shortest distance along cone

1. May 19, 2009

abcd999

1. The problem statement, all variables and given/known data
Obtain an integral formula for the length of a curve p(theta) along a right cone. use spherical coordinates p and theta.
Answer: L = integral from -pi/2 to pi/2 of sqrt(p'^2 + p^2/R^2)d(theta)

2. Relevant equations
p is distance from origin
altitude a, radius 1, cone's point is at origin, R=sqrt(a^2+1)

3. The attempt at a solution
I know ds^2 = dp^2 +sin^2p d(theta)^2 on spherical coordinates, but don't know how to begin translating that into the answer above

Last edited: May 19, 2009