   Chapter 10.5, Problem 62E

Chapter
Section
Textbook Problem

# (a) If an ellipse is rotated about its major axis, find the volume of the resulting solid. (b) If it is rotated about its minor axis, find the resulting volume.

(a)

To determine

To Find: The volume of the resulting solid if an ellipse is rotated about its major axis.

Explanation

Given:

The ellipse is rotated about its major axis.

Calculation

The equation of the ellipse is x2a2+y2b2=1 .

Rewrite the above equation as,

y2b2=1x2a2y2=(1x2a2)×b2y=(1x2a2)×b2y=(a2x2a2)×b2

y=b2a2(a2x2)y=±baa2x2

Compute the volume of the ellipse if it rotated about it major axis.

V=aaπy2dx .

Substitute baa2x2 for y

b)

To determine

To Find: The volume of the resulting solid if an ellipse is rotated about its minor axis.

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