SOLUTION: Find the surface area of a torus (doughnut) obtained by rotating the circle (x-b)^2+y^2 = a^2 about the y-axis.

Algebra ->  Surface-area -> SOLUTION: Find the surface area of a torus (doughnut) obtained by rotating the circle (x-b)^2+y^2 = a^2 about the y-axis.      Log On


   



Question 341303: Find the surface area of a torus (doughnut) obtained by rotating the circle (x-b)^2+y^2 = a^2
about the y-axis.

Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
The center of the circle is b units from the origin. The circle has radius a.
The circle has circumference 2%2Api%2Aa
It travels a distance 2%2Api%2Ab around the y-axis.
By the Second Theorem of Pappus:
the surface area is %282%2Api%2Aa%29%282%2Api%2Ab%29=4%2Api%5E2%2Aa%2Ab