Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347



Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Investigation The top outer edge of a solid with vertical sides and resting on the xy-plane is modeled by r ( t ) = 3 cos t i + 3 sin t j + ( 1 + sin 2 2 t ) k , where all measurements are in centimeters. The intersection of the plane y = b , where ( 3 < b < 3 ) with the top of the solid is a horizontal line.

(a) Use a computer algebra system to graph the solid.

(b) Use a computer algebra system to approximate the lateral surface area of the solid.

(c) Find (if possible) the volume of the solid.


To determine

To graph: The solid modeled by the function r(t)=3costi^+3sintj^+(1+sin22t)k^ by the use of a Computer algebra system



The top outer edge of a solid with vertical sides and resting on the xy-plane is modeled by

r(t)=3costi^+3sintj^+(1+sin22t)k^ and all measurements are in centimeters. The

intersection of the plane y=b(3<b<3) with the top of the solid is a horizontal line.


Compare r(t)=3costi^+3sintj^+(1+sin22t)k^ with the standard equation r(t)=(xt)i^+y(t)j^+z(t)k^, That is





The plane y=b, where 3<b<3, is constant


To determine

To calculate: The lateral surface area of the obtained solid approximately by using a CAS.


To determine

To calculate: The volume of the solid which is obtained in the above part.

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Chapter 15 Solutions

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