The equation is x y2b and on right it read 054 b Determine

The equation is x = (y^2)/b and on right it read 0.54 b.   Determine the y-coordinate of the centroid of the shaded area.

Please show all steps.

Your answer is incorrect. Try again. Determine the y-coordinate of the centrold of the shaded area. 0.54b

Solution

The centroid is found using the are moment method where the shaded area moment about the y axis is calculated.

The area of the shaded region is given by,

area of half semi circle - area of triangle = pi r^2 - 0.5 x a x 0.46b = 3.14r^2 - 0.26^2 ( a = b = r )

The area moment of the section is given by,

moment of half semi circle about the y axis - moment of triangle about the y axis

pi x r^2 x r / 2 - 0.5 x r x 0.46 r x 0.46r / 2

1.57 r^3 - 0.0676 r^3 = 1.636 r^3

Now the ratio of the area moment to the shaded area gives the centroid,

1.636r^3 / 2.88r^2 = 0.56r