Let T be a circle with diameter AC=a, and let B be a point on T such that AB=b<a. Let T' be the semicircle with diameter AC in the plane perpendicular to that of T.
Rotating T' around the perpendicular at A to the plane ABC generates a torus of internal radius 0. Give the equation of .
I've started by drawing everything out. If the circle is in the x-y plane, with the point A as at the origin, then the perpendicular is the z axis and the semi circle T' is in the x-z plane. Rotating around the z axis I can't see how this produces a torus? At best I get an upper half of a torus?
Edit: There also seems to be redundant information there. Multipart question?
Thanks, I think what they want is to extend the semi-circle to a circle in the x-z plane, rotate it, give the equation of the resulting torus and then for the following parts only consider the upper half.
Archytas' solution to doubling the cube if you're interested.