Problem:
Six pepperoni circles will exactly fit across the diameter of a -inch pizza when placed as shown. If a total of circles of pepperoni are placed on this pizza without overlap, what fraction of the pizza is covered by pepperoni?
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Solution:
If six pepperonis fit across the diameter, then each pepperoni circle has a diameter of inches and a radius of inch. The area of each pepperoni is square inches. The pepperoni circles cover square inches of the pizza. The area of the pizza is square inches. The fraction of the pizza covered by pepperoni is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions