Question

Which pizza store offers a better deal on pizza/dollar and how much pizza do you get per dollar? *The amount of pizza is sector area.

Mama John's: A 30-degree slice from a 12-inch diameter pizza for $4.
Big Caesar's: A 45-degree slice from a 10-inch diameter pizza for $3.50.
a) Mama John's: more pizza per dollar
b) Big Caesar's: more pizza per dollar
c) Both offer the same pizza per dollar
d) Cannot be determined with given information

Answer 1

Big Caesar's offers a better deal with approximately 0.8928π square inches of pizza per dollar compared to Mama John's, which offers 0.75π square inches per dollar.

Step-by-step explanation:

To determine which pizza store offers a better deal on pizza per dollar, we need to calculate the sector area of each slice and divide it by the cost of that slice.

Mama John's slice is from a 12-inch diameter pizza, making the radius 6 inches (12 inches/2). The area of the whole pizza is A = π * r^2 = π * 6^2 = 36π square inches. The sector area for a 30-degree slice is (30/360) * 36π = 3π square inches. Since the slice costs $4, you get 3π/4 square inches per dollar.

Big Caesar's slice is from a 10-inch diameter pizza, making the radius 5 inches. The area of the whole pizza is A = π * r^2 = π * 5^2 = 25π square inches. The sector area for a 45-degree slice is (45/360) * 25π = (1/8) * 25π = 3.125π square inches. Since the slice costs $3.50, you get 3.125π/3.50 square inches per dollar.

Comparing the two:

• Mama John's: 3π/4 ≈ 0.75π square inches per dollar
• Big Caesar's: 3.125π/3.50 ≈ 0.8928π square inches per dollar

Therefore, Big Caesar's offers more pizza per dollar than Mama John's (Option b).