Calc 2 Urgent Surface Area
posted by Melissa
Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis.
We have to use the surface area formula.
surface area formula? There are probably thousands of them. Cal 2, I assume you are doing integration.
However, the surface area formula of a cone strikes me quickly. Here you have a base cone of radius 4, and altitude of 1.
SA=PI*r (r+ sqrt(r^2+h^2))
Oh yeah. Sorry I did the volume instead.
Consider the surface as a pile of circular rings, each with circumference 2πr. So, the surface area is
S = ∫[0,1] 2πx ds
but ds is a small piece of the line, of length ds^2 = dx^2+dy^2 = dx^2 + (4dx)^2 = 5dx^2
S = ∫[0,1] 2πx√5 dx = √5 π
This is the lateral area as given by bobpursley above. He also included the base of the cone, but we do not want that for the surface of revolution.