# How to compute the max/min surface area of a donut-shape solid generated by a revolved 2D circle, as the volume of the solid doesn’t change?

A donut shape solid is generated by revolving a circle $$(x-a)^2+y^2=b^2$$ around the y-axis. $$a$$ is the distance from the center of the hole of the donut to the center of the circle revolved, and $$b$$ is the radius of the circle revolved. I’m trying to compute the minimized surface area and the maximized surface area (if the solid has) with the value of $$a$$ and $$b$$, while the volume of the solid doesn’t change (which is $$90\pi^2$$). Thanks a lot if someone can help me 🙂