Finding the Centre of Mass of a Cubical Container

[suspenc3]

A cubical container has been constructed from metal plate of uniform density and negligible thickness. The box has an edge length of 40 cm.

Find the x, y, & z coordinates of the centre of mass of the box.

Im guessing that the x and y coordinates are found by the symmetry..But how do i find the y coordinate?

Any help would be appreciated

 

[suspenc3]

Now that I think about it, Wouldnt the y coordinate 0?

If this is right, is their any method to show my work, or is it all just found by symmetry?

 

[Tubs]

A cubical container has been constructed from metal plate of uniform density and negligible thickness. The box has an edge length of 40 cm.
Find the x, y, & z coordinates of the centre of mass of the box.
Im guessing that the x and y coordinates are found by the symmetry..But how do i find the y coordinate?
Any help would be appreciated

I'm guessing you mean how do you find the z coordinate. Since a box has uniform length in every dimension it is easy to find the COM in every component through symmetry.

 

[suspenc3]

what I meant was : "remember that the box has no top
I can find the centre of mass in the x & z directions through symmetry

How do i find the y component? then i thought about it and realized that it would be "0"...therefore the centre of mass is (20, 0, 20)?

How do I show work for this?