A pizza restaurant offers two sizes of pizzas: small and large. The small pizza costs $12 and has a diameter of 10 inches, while the large pizza costs $18 and has a diameter of 16 inches. If the cost of ingredients per square inch for both sizes is the same, which pizza size provides more value for the money?
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Small pizza
Large pizza
They are equal in value
To determine which pizza size provides more value for the money, we need to calculate the cost per square inch for both sizes.
The area of a circle is calculated using the formula A = πr^2, where r is the radius of the circle. Since the diameter of the small pizza is 10 inches, the radius is 10/2 = 5 inches. Similarly, for the large pizza, the radius is 16/2 = 8 inches.
For the small pizza:
Area = π(5)^2 = 25π square inches
Cost per square inch = $12 / (25π) ≈ $0.076 per square inch
For the large pizza:
Area = π(8)^2 = 64π square inches
Cost per square inch = $18 / (64π) ≈ $0.089 per square inch
Since the cost per square inch for the small pizza is lower than that of the large pizza, the small pizza provides more value for the money.