1. (15 points) Consider the three-dimensional space with line element ds² = dr2 1-2M/r + r² (do² + sin² Odo²). This describes the spatial part of the Schwarzschild black-hole space- time geometry (a two dimensional slice appears in the cover of Hartle's book). Calculate the following quantities: (a) the area of a sphere of coordinate radius r = R; (b) the 3-volume of a sphere of coordinate radius r = R;