   Chapter 10.3, Problem 65E

Chapter
Section
Textbook Problem

Surface Area In Exercises 63-68, find the area of the surface generated by revolving the curve about each given axis. x = 5 cos θ , y = 5 sin θ , 0 ≤ θ ≤ π 2 , y-axis

To determine

To calculate: The surface area of the curve x=5cosθ,y=5sinθ generated by revolving it about y-axis within the interval 0θπ2.

Explanation

Given:

The parametric equations,

x=5cosθy=5sinθ

And, the interval 0θπ2.

Formula used:

The surface area of a smooth curve C given by x=f(t) and y=g(t) generated by revolving the curve C about the y-axis within the interval atb is given by formula:

S=2πabf(t)(dxdt)2+(dydt)2dt

Calculation:

Consider the equations,

x=5cosθy=5sinθ

Differentiate x=5cosθ with respect to ‘θ’, to get,

dxdθ=5sinθ

Differentiate y=5sinθ with respect to ‘θ’, to get,

dydθ=5cosθ

If smooth Curve C given by x=f(t) and y=g(t) does not cross itself on an interval atb

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