This is a simple question that I have done on a test paper, but the given answer is confusing me.
The question states that a person has a bunch of cubes of volume 3 cubic centimetres. The person also has a container of size 6cm x 6cm x 3cm. What is the maximum number of small cubes that can be fit in the large container? No matter how I try I get 36 cubes, but the answer given is 32. How is this so?
Each small cube has a side length of $\sqrt[3]{3}\approx 1.442$ cm. Two cubes would thus fit in the height ($2\sqrt[3]{3}<3$). Four cubes would fit in the length ($4\sqrt[3]{3}<6$) and four cubes would fit in the width. You could thus fit $2\times 4\times 4=32$ small cubes in the container.