CPM Homework Help : INT3 Problem 4-125

The figure at right was created by rotating a two-dimensional shape around two different axes; first the original shape was rotated around one axis then the new solid was rotated around the other axis. Visualize this. Sketch the possible original shape and the two axes. Be sure to position the axes in relation to the shape to create the three-dimensional solid.

Hint:

Think about the first quadrant of a graph. Can you rotate a specific shape $360^\circ$ and formulate the shape depicted?

Answer:

A right triangle can be rotated first about a leg, then the resulting cone would be rotated about an axis lying in the plane of a base, passing through the center.

3 dimensional shape, that has 2 cones, attached at their bases, with top cone shaded light gray & bottom cone shaded dark gray. Dashed ovals, 1 horizontal around the base of the cones, & 1 vertical, so its ends touch the top & bottom vertex of the 2 cones.