"When finding solids of revolution we first evaluate an integral that calculuates the *area under a curve* and then rotate that quantity.
When finding surfaces of revolution we evaluate an integral that calculates the *length of a curve* and then rotate that quantity. "
Agreed, Kyle. My question is - why does the area under the curve calculation ignore the "arc length" aspect. The arc length is used as the basis for the surface area of revolution while the arc length is approximated to the x component while calculating the volume (or the area under the curve). I dont understand how that is justified.