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

Re: find an equation for surface of revolution

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.

Re: find an equation for surface of revolution

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 .

Re: find an equation for surface of revolution

@HallsofIvy thank you that makes perfect sense.