Find the surface area of the part of the plane5 + 7x + 2y that lies inside the cylinderx² + y? = 91019/657

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Find the surface area of the part of the plane z = 5 + 7x + 2y that lies inside the cylinder x² + y? = 9

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 26E

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Question

Find the surface area of the part of the plane
5 + 7x + 2y that lies inside the cylinder
x² + y? = 9
101
9/657

Expert Solution

Step 1

Part of the plane is z = 5 + 7x + 2y, so this is given in terms of f(x,y). If part of the plane is given then formula for calculating surface area is $\iint \sqrt{1 + {(\frac{\partial f (x, y)}{\partial x})}^{2} + {(\frac{\partial f (x, y)}{\partial y})}^{2}} . d A$

We can write z = 5 + 7x + 2y as f(x,y) = 5 + 7x + 2y

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