Apile of earth standing on flat ground near an abandoned mine has height 13 meters. the ground is the xy-plane; the origin is directly below the top of the pile and the z-axis is upward. the cross-section at height z is given by x^2 + y^2 = 13 − z for 0 ≤ z ≤ 13 with x, y, and z in meters. (a) what equation gives the edge of the base of the pile? (b) what is the area of the base of the pile? give an exact answer. (c) what equation gives the cross-section of the pile with the plane z = 10? (d) what is the area of the cross-section in part (c)? give an exact answer. (e) what is a(z), the area of a horizontal cross-section at height z? (f) use your answer to part (e) to evaluate int_0^(13) text( ) a(z)dz. (g) what are the units of your answer in part(f)?