Question

- 4 in. 5. For the composite area shown, the centroid 7 is closest to: a) 0.5 in b) 1.5 in c) 2.5 in d) 3.5 in e) 4.5 in 3 in. 3 in

Answer 1

3 in 3in 4 in 6 A. D F 3 in E 3in --> X C ADE and det us consider a rectangle OABC and subtract the area of triangle area of quarter circle foum it. Then we will get the area of original figure (shape) OEDFGC. 10 in A 3in D B A2 3in Az Gin E 3 in det, unea area of rectangle O ABC is Ay and centroid from origin is you of triangle ADE is Az and centroid from origin is area of quarter circle is Az and centroid from origin is Y A. = 10x6 in A2 = {*3*3 in?! Az = x(3? in? y, = 6 in yz 42 ={*)+ 0 € (3-4x)+(9 So, 2 43 = (3- 4x3 + CG y- 5 in 3R 43 = 1.72 +3 Y = 4.72 in 502 y (from origin ) = Ay, +42)42 + (-43); A,+ (- A2)+(-43) --ve sign shows that area A, and Az ar subtracted or veduced,

Now, اعه (10x6xų) - (* *3*3*5) - ( 5 x 3² x 4.42) (1046) - (x3x3) - x3) 180- 22.5 33.36 as 60 - 4.5 - 7:06 2,56 in foom origin Hence, The centroid of the composite avea lies on 2.56 in from origin. Hence, Option (©) is correct.

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