- #1
toforfiltum
- 341
- 4
Homework Statement
Suppose that a surface has an equation in cylindrical coordinates of the form ##z=f(r)##. Explain why it must be a surface of revolution.
Homework Equations
The Attempt at a Solution
I consider ##z=f(r)## in terms of spherical coordinates.
## p cosφ = f \sqrt{(p sinφcosθ)^2 + (p sinφsinθ)^2} ##
## p cosφ= f\sqrt{(p sinφ)^2} ##
## p cosφ=f(p sinφ)##
##cosφ= f (sinφ)##
##∴φ= \cos^{-1} f(sinφ)##
Since equation is independent of ##\theta##, it describes a surface of revolution about the ##z## axis.
Is my prove right or acceptable?