   Chapter 10.1, Problem 72E

Chapter
Section
Textbook Problem

# Surface Area A satellite signal receiving dish is formed by revolving the parabola given by x 2 = 20 y about the y-axis. The radius of the dish is r feet. Verify that the surface area of the dish is given by 2 π ∫ 0 t x 1 + ( x 10 ) 2 d x = π 15 [ ( 100 + r 2 ) 3 / 2 − 1000 ]

To determine

To prove: That the surface area of the dish provided by the expression 2π0rx1+(x10)2dx=π15[(100+r2)321000].

Explanation

Given: A spherical dish of radius r is formed by revolving the parabola x2=20y around y- axis

Formula used: The surface of revolution of a curve around y axis is provided as, 2πbbx1+(y)2dy

Proof: The surface of revolution of any curve around y axis is given by 2πbbx1+(y)2dy

Here,

x2=20yy=x220y=x10

So, the surface of revolution in this case is given by,

=2π0rx1+(x10)2dx=2π0r

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