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))
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.
2 answers
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.
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.