A cone can be made by rotating a triangle! The triangle is a right-angled triangle, and it gets rotated around one of its two short sides. The side it rotates around is the axis of the cone.
When the two bases are exactly over each other and the axis is a right angles to the base, this is a called a 'right cylinder'. Rectangles can be rotated to make cylinders.
A sphere is created when a circle is rotated in space about one of its diameters. A sphere is the set of all points in space that are a given distance (radius) from a given point (center). The intersection of a plane through the center of a sphere is known as a great circle. figure below.