Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....  # Scaling of a more complex shape o / The 48-point "S" has 1.78 times more area than the 36-point "S."

The first letter "S" in figure o is in a 36-point font, the second in 48- point. How many times more ink is required to make the larger "S"? (Points are a unit of length used in typography.)

Correct solution: The amount of ink depends on the area to be covered with ink, and area is proportional to the square of the linear dimensions, so the amount of ink required for the second "S" is greater by a factor of (48/36)2 = 1.78.

Incorrect solution: The length of the curve of the second "S" is longer by a factor of 48/36 = 1.33, so 1.33 times more ink is required.

(The solution is wrong because it assumes incorrectly that the width of the curve is the same in both cases. Actually both the width and the length of the curve are greater by a factor of 48/36, so the area is greater by a factor of (48/36)2 = 1.78.)

Last Update: 2009-06-21