Thinking problem

Question

In a last-ditch attempt to increase their budget, science teachers at CDDHS cast small solid bronze busts of their principal for sale to students as doorstops, paperweights, etc. One order, in suspiciously familiar handwriting, came in for a bust that would be identical except for scale: it was to stand four times as tall as the standard model. How many of the small busts did the teachers have to melt down to cast this big one?

Answer 1

" identical except for scale" and "four times as tall" also means four times as long and four times as wide.

Consider a block that is 1" x 1" x 1" and a block that is a similar shape, but four times as tall --

it must be 4" x 4" x 4"

The volume is (4*4*4) / (1*1*1) = 64 times as much (note: "melt down").

The teachers would have to melt down 64 small busts to cast the big one.