# Surface Area of a Solid of Revolution

Surface Area of a Solid of Revolution

This Demonstration shows the approximation steps that lead to the derivation of the general formula for the surface area of a solid of revolution about the axis: .The first view (solid) shows that the surface is a union of bands like the one swept out by the arc PQ. The second view (frustum of a cone) shows how the line segment joining P and Q sweeps out a frustum of a cone. The last view (arc length) shows the dimensions associated with the arc and line segment PQ.

x

S=2πy

b

∫

a

1+

dx2

dy

dx