Chapter 16.2, Problem 94E

Square region Consider the region

 R = {(x, y): |x| + |y| ≤ 1} shown in the figure.

 a.    Use a double integral to verify that the area of R is 2.

b.    Find the volume of the square column whose base is R and whose upper surface is z = 12 – 3x – 4y.

 c.    Find the volume of the solid above R and beneath the cylinder x² + z² = 1.

d.    Find the volume of the pyramid whose base is R and whose vertex is on the z-axis at (0, 0, 6).