# Scaling up

Here are two related problems, one precise, one an estimation.

1. A sculptor builds a model for a statue of a terrapin to replace Testudo.* She discovers that to cast her small scale model she needs 2 kg of bronze. When she is done, she finds that she can give it two coats of finishing polyurethane varnish using exactly one small can of varnish. The final statue is supposed to be 5 times as large as the model in each dimension. How much bronze will she need? How much varnish should she buy? (*Hint*: If this seems difficult, you might start by writing a simpler question that is simpler to work on before tackling this one.)

2. The human brain has 1000 times the surface area of a mouse's brain. The human brain is convoluted, the mouse's not. To see how much of this is due to convolutions, estimate by what factor the surface area of the human brain would be larger than the mouse's if the human brain were NOT convoluted. How sensitive is your result to your estimations of the approximate dimensions of a human and mouse brain?

* Testudo is the statue of a Terrapin (the university mascot) in front of the main library on the University of Maryland campus.

Joe Redish 9/30/04

Last Modified: May 19, 2021