Explanation Given information: Thesolid figure of square of size L is revolved about a line that is outside the square, parallel to two of its sides, and located s units from the closer side. Formula used: Theorem of Pappus: The solid generated by revolving a region R about a line outside its boundary has volume V = A s , where A is the area of R and s is the distance travelled by the centroid of R. Calculation: Side of the equilateral triangleis L. To find the height, h, by using hypotenuse formula, we get h = L 2 − ( L 2 ) 2 = 3 2 L Area of the regionisthe area of the equilateral trianglewhich is given by A r e a = 1 2 ( b a s e ) ( h e i g h t ) = 1 2 ( L ) ( 3 2 L ) = 3 4 L 2 Centroid of an equilateral triangle with side L is ( x ¯ ,

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 6.5, Problem 60PS

To determine

To compute:The volume of the solid figure generated when an equilateral triangle ofside L is revolve about one of its side.

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Chapter 6.5, Problem 59PS

Chapter 6.6, Problem 1PS

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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The volume of the solid figure generated when an equilateral triangle ofside L is revolve about one of its side.

Solution Summary: The author calculates the volume of the solid generated when an equilateral triangle of side L is revolved about a line that is outside the square, parallel to two of its sides.

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To compute:The volume of the solid figure generated when an equilateral triangle ofside L is revolve about one of its side.

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Chapter 6 Solutions