Chapter 1.9, Problem 1A

Tennis balls are packaged in a cylindrical can, and since they're round, that leaves a lot of empty space in the can. How much space? The radius of a tennis ball is 3.3 cm; the can has the same radius for a nice tight fit, and the height of the can is six times that radius, which is 19.8 cm.

The calculation below is intended to find the volume of the empty space in the can, but there’s something wrong with it. Explain how you can tell without doing any calculations or looking up any formulas that the answer will be wrong. (Hint: The terms “units” and “like terms” might come into play.)

$\text{Volume}=\underset{\text{Volume}\text{of}\text{can}}{\underset{︸}{\pi {\left(3.3\text{cm}\right)}^2\left(19.8\text{cm}\right)}}-3\left(\underset{\text{Volume}\text{of}\text{each}\text{ball}}{\underset{︸}{\frac{4}{3}\pi {\left(3.3\text{cm}\right)}^2}}\right)$