(a) Explanation Given information: The solid is formed by revolving around the y- axis. The region bounded by the curves y = ± 4 x and the lines x = 1 and x = 4 . Calculation: Provide the equation of curve as shown below. y = 4 x y = − 4 x The radius of the shell is x . Calculate the shell height as shown below. Shell height = 4 x − ( − 4 x ) = 8 x Calculate the volume of the solid using shell method as shown below. V = ∫ a b 2 π ( shell radius ) ( shell height ) d x Substitute 1 for a , 4 for b , x for shell radius, and 8 x for shell height (b) To determine Calculate the center of mass of a thin plate. (c) To determine Sketch the thin plate with the center of mass.

Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)

14th Edition

ISBN: 9780134439419

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Question

Chapter 6.6, Problem 25E

(a)

To determine

Calculate the volume of the solid.

(b)

To determine

Calculate the center of mass of a thin plate.

(c)

To determine

Sketch the thin plate with the center of mass.

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Chapter 6.6, Problem 24E

Chapter 6.6, Problem 26E

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Thomas' Calculus: Early Transcendentals, Single Variable (14th Edition)

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