Expert: Scott A Wilson - 3/13/2011

Question
Scott! A little help here? :)
If 64 tiny squares make a square inch, how many tiny squares will make a cubic foot? (Hint: How many tiny squares are in each inch?)

Hope you can do it! Thanks!

Answer
If 64 make a square inch, that means they are 1/8" long and wide,
so they fit in a pattern that is 8x8=64 and 1"x1".

If we are talking about a cubic foot (volume instead of area),
and an area with a foot on a side instead of an inch, that means two things.
One, we have to multiply 8 square x 12 inches to get 96 squares that would fit on each edge.
Since the edges go in three directions, take 96 x 96 x 96.

Now that is the same as taking (100-4)^3 = 100^3 - 3*4*100^2 + 3*4^2*100 - 4^3.
That is, 1,000,000 - 120,000 + 4,800 - 64.
That is 880,000 + 4,736 = 884,736.