Puzzle ZWSK 

Workings

Hint
A little algebra might help.

Answer
Width=40, height=20, depth=18.

Reasoning
If we call the height H, the width W and the depth D we have:
   H x W = 800

       H = 800 ÷ W (1)

   W x D = 720

       W = 720 ÷ D (2)

   H x D = 360

       H = 360 ÷ D (3)

Using (1) and (3) we have:
   800   360
   ——— = ———
    W     D

   800 x D = 360 x W

Using (2):
   800 x D = 360 x 720
                   ———
                    D

   800 x D² = 259,200

         D² = 324

          D = 18

Using (2), W = 40.

Using (1), H = 20.