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From the rectangular area shown a semi-circle of radius 4 cm is removed. Locate the centroid, (C), of the remaining area. [Ans. C: (3.70m, 0)] y 6m 4cm 6m

From the rectangular area shown a semi-circle of radius 4 cm is removed. Locate the centroid, (C), of the remaining area. [Ans. C: (3.70m, 0)] y 6m 4cm 6m

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter8: Centroids And Distributed Loads
Section: Chapter Questions
Problem 8.136RP: Calculate the area of the surface generated when the plane z-curve is rotated about (a) the x-axis;...
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" Centroids "

I just want to clarify Because I get the answer approximately 3m and the answer key was 3.70 and the expert answered 3.69 which is correct also based on answer key but my issue here is that the radius is in the unit of "Centimeter" i converted it to meter and thats the thing i got different with the solution of expert, maybe the radius should be in meter because the units used is meters? I want to correct myself or to clarify maybe the answer key was wrong If i should convert the CM to M or let it as it should be in cm? Thankyouuu! I appreciate your effort in helping and answering me!

From the rectangular area shown a semi-circle of radius 4 cm is removed. Locate the centroid, (C), of the remaining area. [Ans. C: (3.70m, 0)] y 6m X X 4cm 6m 6m
Transcribed Image Text:From the rectangular area shown a semi-circle of radius 4 cm is removed. Locate the centroid, (C), of the remaining area. [Ans. C: (3.70m, 0)] y 6m X X 4cm 6m 6m
We know that after removing any area from a given area, the centroid can be calculated from the given formula Xem = A-Ag total area Here A, A2 = removed area x1 &x2 are the distances of centroid from a fixed origin for the respective areas Now A, = area of rectangle = 6x 12 = 72 m? Also A2 area of semicircle = 0. Sm? = 0. 5m x 4? = 25. 13 m? X1 = centroid of rectangle measured from origin O = 3m X2 = centroid of semicircle measured from origin O = 6 = 6 - 37 - 4x4 = 6 16 = 4. 302 m. - After putting all the values we get 72x3 - 25.13x4302 Kam = = 2. 3019 m 72-25.13 Calculating xem from the center of the semicircle is 6– 2. 3019 = 3. 698 As the figure is symmetric about x axis thus yam = 0 Hence Centroid = C(3. 69,0)
Transcribed Image Text:We know that after removing any area from a given area, the centroid can be calculated from the given formula Xem = A-Ag total area Here A, A2 = removed area x1 &x2 are the distances of centroid from a fixed origin for the respective areas Now A, = area of rectangle = 6x 12 = 72 m? Also A2 area of semicircle = 0. Sm? = 0. 5m x 4? = 25. 13 m? X1 = centroid of rectangle measured from origin O = 3m X2 = centroid of semicircle measured from origin O = 6 = 6 - 37 - 4x4 = 6 16 = 4. 302 m. - After putting all the values we get 72x3 - 25.13x4302 Kam = = 2. 3019 m 72-25.13 Calculating xem from the center of the semicircle is 6– 2. 3019 = 3. 698 As the figure is symmetric about x axis thus yam = 0 Hence Centroid = C(3. 69,0)
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