Center of Mass for a cubical box with a missing top

1. The problem statement, all variables and given/known data
A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L=40cm. Find (a) the x coordinate (b) the y coordinate, and (c) the z coordinate of the center of mass of the box.

Ok, so my professor already worked this problem for us, but I have no clue what she did.

2. Relevant equations

3. The attempt at a solution
L=40 cm=0.4 m

Then she divided that by two for some reason?
Front and Back center of mass: (0.2, 0.2, 0.2)
Right and Left center of mass: (0.2, 0.2, 0.2)
Top and Bottom (top is missing): (0.2 ,0.2 , 0)

xcm=[itex]\frac{1}{5m}[/itex](2m(0.2)+2m(0.2)+m(0.2))=0.2m
ycm=[itex]\frac{1}{5m}[/itex](2m(0.2)+2m(0.2)+m(0.2))=0.2m
zcm=[itex]\frac{1}{5m}[/itex](2m(0.2)+2m(0.2)+m(0))=0.16m

I am so confused! Can someone please explain to me what she did? Is there a formula that she used? I looked in my book and the only one I found needed the mass to use it.

http://ift.tt/O1ObHg

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