   Chapter 15, Problem 44RE

Chapter
Section
Textbook Problem

Find the area of the part of the cone z2 = a2(x2 + y2) between the planes z = 1 and z = 2.

To determine

To find: The area of the given region.

Explanation

Formula used:

The surface area with equation z=f(x,y),(x,y)D , where fx and fy are continuous, is A(S)=D[fx(x,y)]2+[fy(x,y)]2+1dA .

Here, D is the given region.

Given:

The part of the cone z2=a2(x2+y2) between the planes z=1,z=2 .

Calculation:

z varies from 1 to 2 and z2=a2(x2+y2) .

z2a2=x2+y2x2+y2=z2a2x2+y2=1a2        [when z=1]x2+y2=4a2        [when z=2]

Thus, the region lies between two annular region of radius 1a2 and 4a2

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