Problem of the Week 1002

How Much Chocolate?

A round cookie of radius 1 inch is rolled 30 degrees in each direction in a pan containing chocolate to a depth of 1/2 inch. What is the area of the disk that is covered in chocolate?

Source: Tom Pfaff, Ithaca College, in College Math Journal, Nov. 2003, p. 406. This is a live problem, so we will not give out solution comments. Interested readers can submit their solution to the CMJ.

More precision: The cookie is viewed as an infinitely thin disk of radius 1 centered at (0,1). It is rolled along the x-axis 30 degrees in each direction. Any part of the disk that comes into contact with the strip 0 ≤ y ≤ 1/2 gets covered in chocolate.

© Copyright 2004 Stan Wagon. Reproduced with permission.

17 February 2004