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 of revolution.
integral (2pi*f(x)sqrt(1+f'(x)^2))dx

Use the first Pappus theorem for the surface area.
dA = 2πR(dS)
where R = the distance between the centroid of the surface plane to the line of revolution
dS = infinitesimal arc length
dA = infinitesimal area

We integrate it to get the whole surface area. For more info, refer on the image as you can see labels and solutions.

The answer for this question is 80