volume and surface area

Question

Describe, in a series of steps, how you would help a student “see” how many cubic centimeters are in a cubic meter. Assume that you have a meterstick and centimeter cubes.

Answer 1

Hi Karen P.,

If you had enough cubes (1,000,000 of them) you could stack them up as a 100 x 100 x 100 cubic block. I really don't recommend this, particularly if you have any rowdy colleagues (classmates) anywhere near you. Also, since the density of (oak, for example) is ~770 kg/m^3, that might collapse your lab table. But you might lay out 100 x 1 and 1 x 100 at right angles to each other, sharing the corner block, and then a few blocks stacked on top of that corner, and say "Just imagine ...."

Or, temporarily tape 12 meter sticks together to comprise the edges of a 1m x 1m x 1m cube, and put a single 1 cm x 1 cm x 1cm block inside, and say, "imagine this cube completely filled with the small blocks".

Extender question: Air has mass! So how much does 1 m^3 of air weigh? The answer may surprise you: a bit over 1 kg. How come you don't perceive that in your daily life?

Cheers, -- Mr. d.