   Chapter 10.5, Problem 68E

Chapter
Section
Textbook Problem

# Finding the Area of a Surface of Revolution In Exercises 69 and 70, use the integration capabilities of a graphing utility to approximate the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = θ ,       [ 0 , π ]

To determine

To Calculate: The area of surface formed by revolving the polar equation over the given interval about the polar axis by using the integration capabilities of graphing utility.

Explanation

Given:

Polar equation is given r=θ and the interval 0θπ and the axis of revolution is polar axis.

Formula Used:

s=2παβf(θ).sinθ(f(θ))2+(f'(θ))2.dθ

Calculation:

Consider the polar equation is r=θ where interval is 0θπ and the axis of revolution is polar axis.

It is known that that area of surface will be given by below formula:

s=2παβf(θ).sinθ(f(θ))2+(f'(θ))2

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