   Chapter 12.6, Problem 43E

Chapter
Section
Textbook Problem

# Sketch the region bounded by the surfaces z =  x 2  +  y 2 and x2 + y2 = 1 for 1 ≤ z ≤ 2.

To determine

To sketch: The region bounded by the surfaces z=x2+y2 and x2+y2=1 for 1z2 .

Explanation

Given data:

Surface equations are z=x2+y2 and x2+y2=1 .

Formula used:

Consider the standard equation of circular cone along the z axis.

z2c2=x2a2+y2b2 (1)

Consider the given surface equation.

z=x2+y2

Take square on both sides.

z2=(x2+y2)2z2=x2+y2

z21=x21+y21 (2)

By comparing equation (2) with (1), the given surface equation satisfies the equation of a circular cone along the z-axis.

Find a, b, and c by comparing equation (2) with equation (1).

a2=1a=1a=±1

The value of a is ±1 .

b2=1b=1b=±1

The value of b is ±1 .

c2=1c=1c=±1

The value of c is ±1 .

Case i:

Let x=k

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