Thread: find surface area of a donut

I have a problem where i dont even know where to begin. Usually, when i post problems here i have something to show but this time i dont. Im sorry for that.


here is the problem:

FInd the surface area of the torus (or donut) obtained by rotating the circle (x - b)2 + y2 = a2; (a < b) about the
y-axis.


would i do something like the Area of a surface of revolution theorem?:



if so i am not even sure what to do to get it into the form to put it into that formula?

Any help is appreciated since i am lost!!

Thank you

Originally Posted by icelated

FInd the surface area of the torus (or donut) obtained by rotating the circle (x - b)2 + y2 = a2; (a < b) about the y-axis.

Use the First Guldin Theorem: the surface area of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance traveled by the curve's geometric centroid .

Originally Posted by FernandoRevilla

Use the First Guldin Theorem:

Im not suppose to use pappus's theorem. When i googled First Guldin Theorem everything came back to pappus. What is First Guldin Theorem? =(