Final answer:
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).