Question

A cashier is unsure whether a group of customers ordered and ate a large or a medium pizza. Medium pizzas have a diameter of 12 inches and large pizzas have a diameter of 16 inches. All that remains is one crust that has an arc length of 4.25 inches. All pizzas are divided into 12 equal slices. What size did the customers order? Explain how you determined your answer. That’s the interesting part, because although only one answer exists, you can solve this problem in different ways.A cashier is unsure whether a group of customers ordered and ate a large or a medium pizza. Medium pizzas have a diameter of 12 inches and large pizzas have a diameter of 16 inches. All that remains is one crust that has an arc length of 4.25 inches. All pizzas are divided into 12 equal slices. What size did the customers order? Explain how you determined your answer. That’s the interesting part, because although only one answer exists, you can solve this problem in different ways.

Answer 1

Answer: large pizza

Work:


1) You can determine the arc of a slice that is 1/12 of the whole pizza using the diameter.

2) First, calculate the total circumference of each pizza.

Formula for the circumference: 2π×radius

radius = diameter / 2

medium pizza: 2π (12 / 2) = 12π ≈ 37.70 in

large pizza: 2π (16/2) = 16π ≈ 50.27 in

3) arc of a 1/12 sector

arc of a 1/12 sector = circumferece × 1/12

medium pizza: 37.70 in / 12 = 3.14 in


large pizza: 50.27 in / 12 = 4.19 ↔ this is pretty close to 4.25


So, at the end we have found that the sector of 4.25 in left belongs to a large pizza.