Explanation Given: Tin has 16 cm on a side. A rectangular corner of area 156 cm 2 The centroid of the portion that remains is 4.88 cm from one side of the original square. Calculation: Partition the remaining region into two rectangles. Call them A and B. Let the length and the width of rectangle A be 16 cm and x cm respectively and let the length and the width of rectangle B be y cm and 16 − x cm respectively. Then the coordinates of the centroid C 1 of region A are ( x 2 , 8 ) and the coordinates of the centroid C 2 of region B are ( x + 16 − x 2 , y 2 ) . Moreover, the area of region A is A 1 = 16 x and the area of region B is A 2 = y ( 16 − x ) . Thus the total area is A = 16 ( x + y ) − x y . However, it can also be deducted that A = 256 − 156 = 100 . Thus the coordinates of the centroid C ( x ¯ , y ¯ ) of the entire region (A and B combined) is x ¯ = x 2 A 1 + ( x + 16 − x 2 ) A 2 100 = 8 x 2 + ( x 2 + 8 ) ( 16 y − x y ) 100

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6, Problem 73SP

To determine

To find:the distance from the centroid from the other three sides.

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Chapter 6, Problem 72SP

Chapter 6, Problem 74SP

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 distance from the centroid from the other three sides.

Solution Summary: The author divides the remaining region into two rectangles, called A and B, and deduces that A=256-156=100.

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To find:the distance from the centroid from the other three sides.

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Chapter 6 Solutions