Hi everyone, I'm pretty new to Physics Forums but it seems like a fairly friendly community. :)(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Determine the equation of the surface formed when the line x=3y is rotated about the x-axis.

2. Relevant equations

x=3y is the given line.

3. The attempt at a solution

First I write it in terms of x because it's simpler: [tex]y = \frac{1}{3} x[/tex]

The slope is 1/3, thus, and you have a diagonal line that passes through the origin in a 2-D graph with the X-Y plane.

Now, if you rotate this about the X-axis, you see you get a sort of cone. rather, two cones, one for each side of the y-axis ; these two cones have their tops(tips) facing each other.

How, though, can I determine an equation for the cone? I know there is a generic equation that involves x,y,z variables and a,b,c constants (I think it's something like.. [tex](x-a)^{2} + (y-b)^{2} = (z-c)^{2}[/tex] )

but what do I plug in for the variables and constants? I think I need to substitute [tex]\frac{x}{3}[/tex] for [tex] x [/tex] , or maybe with one of the other variables (y or z) but I'm not sure where and how.

If anyone could help me on this I would very much appreciate it. Thank you!! :)

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Homework Help: 3D Surfaces - Equation Formed When Rotating a 2D Line About an Axis?

**Physics Forums | Science Articles, Homework Help, Discussion**