Explanation If a line fixed at a point is rotated around an axis then it results in a circle whose radius is equal to the length of the line segment. Thus, for a circle with radius r , the area swept is given by A = π r 2 Given: A line segment c ( t ) = ( 3 , t ) ; for 0 ≤ t ≤ 2 Formula Used: For a given curve c ( t ) = ( x ( t ) , y ( t ) ) ; s = ∫ a b x ' ( t ) 2 + y ' ( t ) 2 d t and A = π r 2 Calculation: Given, line c ( t ) = ( 3 , t ) ; for 0 ≤ t ≤ 2 . Here, x ( t ) = 3 and y ( t ) = t ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 12.2, Problem 6PQ

To determine

To determine:

The resulting surface area if the given line segment $c (t) = (3, t);$ for $0 \leq t \leq 2$ is rotated around x-axis.

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Chapter 12.2, Problem 5PQ

Chapter 12.2, Problem 1E

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The resulting surface area if the given line segment c ( t ) = ( 3 , t ) ; for 0 ≤ t ≤ 2 is rotated around x-axis.

Solution Summary: The author calculates the surface area of a circle whose radius is equal to the length of the line segment.

Concept explainers

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To determine:

The resulting surface area if the given line segment $c (t) = (3, t);$ for $0 \leq t \leq 2$ is rotated around x-axis.

Want to see the full answer?

Chapter 12 Solutions

The resulting surface area if the given line segment c ( t ) = ( 3 , t ) ; for 0 ≤ t ≤ 2 is rotated around x-axis.

Solution Summary: The author calculates the surface area of a circle whose radius is equal to the length of the line segment.

Concept explainers

Videos

To determine: The resulting surface area if the given line segment c(t)=(3,t); for 0≤t≤2 is rotated around x-axis.

Want to see the full answer?

Chapter 12 Solutions

To determine:

The resulting surface area if the given line segment $c (t) = (3, t);$ for $0 \leq t \leq 2$ is rotated around x-axis.