# 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.

1. bobpursley

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))

2. Steve

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.

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