Δίκα δὲ τοῖς μὲν παθοῦσ-
ιν μαθεῖν ἐπιρρέπει
Put two apples in an empty cube box. Add another two. How many apples are there in the box? That was easy. Now, empty the box.
Fill it half full of water. Put an apple on a stick. Poke the apple end of the stick into the water, so the apple is completely submerged. Measure the height of the water line. (Use the side of the cube as your unit. The increase is a fraction.) Calculate the volume of the apple.
Calculate the radius of the apple. Calculate the maximum number of apples that can be fit into the box. Calculate the volume left over. Redo your calculation with apples cut in half. Quartered. In eighths.
What is the volume of the largest cube you can cut out of the apple? How many of these cubes can you fit in the box? How much space will be left over?
