   Chapter 10.5, Problem 63E

Chapter
Section
Textbook Problem

# Finding the Area of a Surface of Revolution In Exercises 65-68, find the area of the surface formed by revolving the polar equation over the given interval about the given line.Polar Equation Interval Axis of Revolution r = 6 cos θ 0 ≤ θ ≤ π 2 Polar axis

To determine

To Calculate: The value of the surface area formed by revolving the polar equation r=6cosθ over the interval 0θπ2 about the line.

Explanation

Given:

The polar equation is given r=6cosθ and the interval 0θπ2 and the axis of revolution is polar axis.

Formula Used:

s=2παβf(θ).sinθ(f(θ))2+(f'(θ))2dθ, 2cosθ.sinθ=sin2θ and cos2θ+sin2θ=1

Calculation:

Given polar equation is r=6cosθ where interval is 0θπ2 and axis of revolution is polar axis.

Now, area of surface will be given by below formula;

s=2παβf(θ).sinθ(f(θ))2+(f'(θ))2dθ

Here,

r=6cosθ, α=0, β=π2

And

drdθ=f(θ)=6sinθ

Substitute these values in the above formula and get;

s=2παβf(;

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