Question

If the shape below is a shaded 2D area, find the area and the y-coordinate of the centroid. If the shape below is a composite volume, find the x- and y-coordinates of the centroid. Include units. Area or x-coordinate:

y-coordinate:

10 in- 4 in 4 in 6 in 4 in

Answer 1

givne object
area of shaded region = 6*2 + 3*4 = 12 + 12 = 24 in
coordinate of centroid from the origin = (x,y,z)
now, x = 10 in

for y and z
y = (6*2*3 + 4*3*2)/(24) = 2.5
z = (4*3*1.5 + 6*2*6)/(24) = 3.75
hence centroid of the shaded area is at(10,2.5,3.75) in

for the whole volume
V = 4*3*10 + 6*4*2 + pi*2^2*4 = 218.26548 in^3
centroid of the figure = (x,y,z)
x = (4*3*10*5 + 6*4*2*8 + pi*4*4*8)/V = 6.35063246 in
y = (4*3*10*2 + 6*4*2*3 + pi*4*4*6)/V = 3.14109631 in
z = (4*3*10*1.5 + 6*4*2*6 + pi*4*4*6)/V = 3.5259487 in