A pile of earth standing on flat ground has height 9 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 $x^2 + y^2 = 9 - z$ for $0 \leq z \leq 9$, with $x, y,$ and $z$ in meters.

(a) What equation gives the edge of the base of the pile?
A. $x + y = 9$
B. $x + y = 3$
C. $x^2 + y^2 = 9$
D. $x^2 + y^2 = 3$
E. None of the above

(b) What is the area of the base of the pile?


(c) What equation gives the cross-section of the pile with the plane $z = 6$?
A. $x^2 + y^2 = 36$
B. $x^2 + y^2 = 3$
C. $x^2 + y^2 = 6$
D. $x^2 + y^2 = \sqrt{3}$
E. None of the above

(d) What is the area of the cross-section $z = 6$ of the pile?


(e) What is $A(z)$, the area of a horizontal cross-section at height $z$?
$A(z) =$ square meters

(f) Use your answer in part (e) to find the volume of the pile.
Volume = cubic meters