Question

Determine the y-coordinate of the centroid of the shaded area. - 13" - - - 13" 13" x = kya - - - - - - L - - - 18"

Answer 1

te <- î I 72-13 + XX13 consider a defferential Element of width elx and height (Y2-y,) at a distance se from y-axis, - 131 area of differential Yay 1 Element dA= (% -4,) dx 21 L Sitges y = { 13" -1 ->x 18" dx se=ky,² y = JI at x= 18 137. - 118 Y,= 13" Y = atba at x=0 y = 13 13=a + bxo =) a=13 at x = 18 y = 26 26= 13 + bx18 b= 13 18 k = Glo 15 359 xk - Hexva dA = ( 13+ x - xelis ) cb *A= Sep = f*=* ( 13+ box - wide x 2) ox total shaded Area, X=0

718 +[18418 + 1 cup 13x18 + line < 1892) A=195'in2 moment of differential Element about we axis dOx = 147+ y 2 ) da 2 = (8,+92) (82-41) dove = 1/2 [ Uz? - y2) ex 3 [1134432) - ( " . x)] dze ** = {(169 + 1622x2 + 2x13m x 19 ]dx = { y see + 1692 +169) dr moment of Shaded postion about ze axis Ox= felux de la qua2 + 469 x +169)dx 2=18 x=0

05 : 3 [1293 + 108 2 + 169x316 69 । 2 / 324 । 169 . (18)2 18 २ 7 3 8- 2788.5 in 3 = 3 - 27885 ♡ -14.3") = y coordinate centorord of Shaded portion