Explanation Given: Let V be the volume of the ramp whose length 6 , width 4 and height 2 . Calculation: The area of cross section perpendicular to x - axis is rectangle of width 4 and height 2 − 1 3 x . So, the volume of ramp is; ⇒ ∫ 0 l 4 ( 2 − 1 3 x ) d x = ∫ 0 6 4 ( 2 − 1 3 x ) d x ( ∵ l = 6 ) On integration within the limits 0 to 6 on To determine (b). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to y - axis. To determine (c). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to z - axis.

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.2, Problem 4E

To determine

(a).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $x$ -axis.

To determine

(b).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $y$ -axis.

To determine

(c).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $z$ -axis.

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Chapter 6.2, Problem 3E

Chapter 6.2, Problem 5E

Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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(a). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to x - axis.

Solution Summary: The author calculates the volume V of the ramp by integrating the area of cross section perpendicular to y - axis.

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(a).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $x$ -axis.

(b).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $y$ -axis.

(c).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $z$ -axis.

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(a). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to x - axis.

Solution Summary: The author calculates the volume V of the ramp by integrating the area of cross section perpendicular to y - axis.

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(a). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to x-axis.

(b). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to y-axis.

(c). Calculate the volume V of the ramp by integrating the area of cross section perpendicular to z-axis.

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Chapter 6 Solutions

(a).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $x$ -axis.

(b).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $y$ -axis.

(c).

Calculate the volume $V$ of the ramp by integrating the area of cross section perpendicular to $z$ -axis.