   Chapter 10.5, Problem 64E

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 = a cos θ 0 ≤ θ ≤ π 2 θ = π 2

To determine

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

Explanation

Given:

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

Formula Used:

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

Calculation:

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

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

s=2παβf(θ)cosθ(f(θ))2+(f'(θ))2dθ

Here, r=acosθ,α=0,β=π2

And

drdθ=f(θ)=asinθ

Substitute these values in the above formula and get;

s=2παβf(θ)

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