Question

2. (10 pts.) Consider a sphere of radius R > 0 and its bounding cylinder with height 2R that is tangent to the sphere precisely in an equatorial great circle (as depicted below)

Answer 1

first We are going to have some rectangle over the sphere where the rectangles are tangent planes of the circle sphere and note that the sphere can be appropriate by the surface generated by the rectangles when the area of individual rectangle become finer and finer. Therefore the area is appropriated by many many tiny rectangle. Now We project those rectangle to the cylinder by light positioned on the z-axis. Now the projection is also a rectangle. First We are going to prove that the rectangles have some area. Let the rectangle on the sphere be i.e a be the side along the longitude side. See the change in the b. Let d be the distance from z axis to the loWer side of the rectangle. [We can choose the loWer side as when the discretization goes to tiny and tiny the length d become equal for any position]. Now