Math CentralQuandaries & Queries


Question from megan, a teacher:

What's the volume of a cube with a side length of 6?

Hi Megan,

You didn't give units so I am going to assume the cube has sides of length 6 inches.

Suppose you have a cubical box, 6 inches on each side and you also have a collection of orange cubical blocks, each block measuring 1 inch on each side. Thus each block is 1 cubic inch. Your task is to fill the box with as many blocks as possible.

Start by placing 6 blocks in the bottom of the box, arranged along one side.


Add a second row of blocks beside the first row and continue until you have the bottom of the box covered by a layer of blocks. How many blocks did you use?

Add a second layer on top of the first and then a third layer and continue until the box is full. How many layers did you make? How many blocks is that in total? This is the number of cubic inches in the box.


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