PROBLEM 4. A CONE IS FLAT. Consider a cone with axis along the z-axis, given in spherical coordinates by = 40, 0 < 40 < a. Give a parametrization of the cone of the form Y(p, 0), where p and are the spherical coordinate parameters. Does this parametrization preserve the distance along either coordinate directions? (You could calculate, or you could reason geometrically.) b. We want to figure out how to parametrize the cone without distortion. So imagine a region D in the (u, v)-plane which in polar coordinates is given by 0 0 B, where 0 < 3 < 2. We want to fold this wedge up into a cone. So we want the radial rays from the origin to map to generators of the cone, preserving distance. Make a sketch of the region D and the cone; for fun take