Answer
American is the better deal.
Work Step by Step
If the slices are the same thickness, it is only necessary to compare the area of the end of each block to determine which slice will contain the most cheese.
Use the formula for the area of a square for the American cheese.
$A=s^2=9^2=81$
Use the formula for the area of a circle for the Provolone cheese. The radius of a circle is half the diameter.
$a=\pi r^2=\pi\times (\frac{10}{2})^2=\pi\times5^2=\pi\times25=78.5$
The area is larger for the American cheese, so it is the better deal.
