Question 9.3E3: Comparing Pizzas Victoria Montoya wishes to order a large ch......
Comparing Pizzas
Victoria Montoya wishes to order a large cheese pizza. She can choose among three pizza parlors in town: Antonio’s, Steve’s, and Dorsey’s. Antonio’s large cheese pizza is a round 16-in.-diameter pizza that sells for $15. Steve’s large cheese pizza is a round 14-in.-diameter pizza that sells for $12. Dorsey’s large cheese pizza is a square 12-in. by 12-in. pizza that sells for $10. All three pizzas have the same thickness. To get the most for her money, from which pizza parlor should Victoria order her pizza?
To determine the best value, we will calculate the cost per square inch of pizza for each of the three pizzas. To do so, we will divide the cost of each pizza by its area. The areas of the two round pizzas can be determined using the formula for the area of a circle, A = \pi r^2. Since the radius is half the diameter, we will use r = 8 and r = 7 for Antonio’s and Steve’s large pizzas, respectively, and we will use the \boxed{\pi} key on our calculator. The area for the square pizza can be determined using the formula for the area of a square, A = s². We will use s = 12.
Area of Antonio’s pizza = \pi r^2 = p(8)^2 = p(64) ≈ 201.06 in.^2
Area of Steve’s pizza = \pi r^2 = p(7)^2 = p(49) ≈ 153.94 in.^2
Area of Dorsey’s pizza = s^2 = (12)^2 = 144 in.^2
Now, to find the cost per square inch of pizza, we will divide the cost of the pizza by the area of the pizza.
Cost per square inch of Antonio’s pizza ≈ \frac{\$15}{201.06 in.^2} ≈ \$0.0746
Thus, Antonio’s pizza costs about $0.0746, or about 7.5 cents, per square inch.
Cost per square inch of Steve’s pizza ≈ \frac{\$12}{153.94 in.^2} ≈ \$0.0780
Thus, Steve’s pizza costs about $0.0780, or about 7.8 cents, per square inch.
Cost per square inch of Dorsey’s pizza = \frac{\$10}{144 in.^2} ≈ \$0.0694
Thus, Dorsey’s pizza costs about $0.0694, or about 6.9 cents, per square inch.
Since the cost per square inch of pizza is the lowest for Dorsey’s pizza, Victoria would get the most pizza for her money by ordering her pizza from Dorsey’s.