A caterer packs a rectangular tray-box tightly with 12 identical large ice blocks and some identical small ice cubes, so that cubes of the same size are stacked directly on top of each other, filling the box exactly to the brim. The figure shows the first layer of cubes packed in the box. (a) How many small ice cubes does the caterer have? (b) The volume of the box is 1536 cm³. The total volume of the 12 large ice blocks is 1/2 of the volume of the box. What is the length of one edge of the small ice cube?
Opening the drawing…
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