Thread: find an equation for surface of revolution

I have a problem where i need to
find the equation for surface of revolution if the generating curve y = 2x + 1, is revolved about the y axis


The book gives this formula for revolving around the y axis



So, wouldnt i just plug y in and square it?
most of the problems have been done this way

Problem is i dont get the right answer.
the answer is



What do i need to do?
Thank you

The equation is that of a pair of cones (or is it a single cone ?) with a common vertex and an axis of symetry along the axis. The cones open away from each other from the common vertex. The in the equation is the radius of the cone and the way that it is written says that it is a function of The radius will be zero when and when (or these coming from the generating line
What you are looking for then is a relationship of the form for some values of and such that and
That turns out to be and when you substitute that into the given equation it simplifies to your given answer.

BobP, mathematically, its a single cone. Each part, that in "standard English" is called a cone, is a "nappe" of that cone.

icelated, the "r(y)" is the function x= f(y) in the plane. Since you are given the line y= 2x+ 1, x= r(y)= (y- 1)/2. That is what should be squared, so that .

@HallsofIvy thank you that makes perfect sense.