UNO High School Problem of the Week Competition
Problem 19
One day after school, you are slicing a 20 inch diameter pizza for a snack. Your first two cuts make a 30 degree slice. You continue making cuts until you have gone around the whole pizza, each time trying to copy the previous slice but accidentally adding 2 degrees each time. In other words, the slices are 30 degrees, 32 degrees, 34 degrees...) What is the area of the smallest slice of pizza?
Solution
Answer: 5pi
After nine slices, you have cut 9 * 30 degrees + 0 degrees + 2 degrees +...+16 degrees = 270 degrees + 18 degress * 4 = 342 degrees, so the leftover slice is 18 degrees, with area 100pi * (18/360) = 5pi.
