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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 equationis 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 formfor some values of
and
such that
and
That turns out to beand 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.