pg. 723, #39 (moderate)

Sketch the region bounded by the surfaces for 0 <= z <= 2.

Solution:

The equation z = sqrt(x^2 + y^2), 0 <= z <= 2 is a solid cone centered at the origin.

The equation x^2 + y^2 = 1 , 0 <= z <= 2 is a cylinder formed by the circle of radius 1, centered at

the origin, and the lines perpendicular to it.

The cone and the cylinder will meet at z = 1. The combination will look like a stadium: