Question 6: Suppose you have a box full rice. To the nearest order of magnitude, your want to estimate the number of rice pieces inside the box. The edge of your box is 1.0 m and you measure a typical rice piece to have a length of about 6 mm and radius of about 2 mm.
Since it is impractical to count rice pieces individually, we will be satisfied by knowing roughly their number.
We know that we have a lot of empty space among rice pieces in the box. To compensate for this empty space and to make our calculation easier, we will overestimate the size of an individual rice piece by assuming that it has uniform square cross sectional area over its length. Furthermore, we will imagine that rice pieces are packed closely in the box Now the estimated number, N, can be found by dividing the volume of the box, Vbox,by the volume of an individual rice piece, Vrice.