   Chapter 10.5, Problem 73E

Chapter
Section
Textbook Problem

# Surface Area of a Torus Find the surface area of the tours generated by revolving the circle given by r = 2 about the line r = 5 sec θ .

To determine

To Calculate: The surface area of a torus generated by revolving the circle given by r=2 about the line given as, r=5secθ.

Explanation

Given:

The circle is given by r=2 and its polar equation is r=5secθ.

Formula Used:

Area of surface of revolution,

Calculation:

Consider the polar equation given as;

r=5secθ and circle is given by r=2.

Then,

Area of surface of revolution,

Now, the required surface area of the given torus is generated by revolving the circle given by r=2 about the line r=5secθ as shown as below:

Here, r=f(θ)=2 and f(θ)=0

Consider the diagram to understand the formula of surface of revolution

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