Answer to the Math Problem of the Week for April 22, 2014

Question: A pepperoni pizza has a radius of 7 inches. Each pepperoni has a diameter of 1 inch. If the pizza is topped with 14 pepperonis, what is the area of the pizza that is not covered by pepperonis?

Answer: 91π/2 or approximately 142.94 square inches

The formula for the area of a circle is Area = pi • radius^2

First we need to find the area of the whole pizza.
The pizza has a radius of 7 inches.

Area of the pizza:   pi • 7^2= 49pi

Each pepperoni has a diameter of 1 inch, meaning that each pepperoni has a radius of 1/2 an inch.

The area of one pepperoni is Area = pi • (1/2)^2 = 1/4 • pi = pi/4

There are 14 pepperonis on the pizza, so the area of the pizza that is covered by pepperonis is 14 • pi/4 = 7π/2 square inches. To find the area of the pizza that is not covered by pepperoni, subtract the amount that is covered by pepperoni from the total.

49pi – 7pi/2 = 91pi/2.

The area of the pizza that is not covered by pepperoni is 91pi/2, or approximately 142.94 square inches.