The 12-inch diameter pizza for $6.99 or the large 14-inch diameter pizza for $7.99
area proportional to d^2
144/6.99 = 20.6
196/7.99 = 24.5
You get more pizza area per dollar for the big one.
To determine which pizza offers a better value, we need to compare the cost per square inch of each option.
First, let's calculate the area of each pizza using the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.
For the 12-inch diameter pizza:
- Radius = diameter/2 = 12/2 = 6 inches
- Area = π(6^2) = 36π square inches
For the 14-inch diameter pizza:
- Radius = diameter/2 = 14/2 = 7 inches
- Area = π(7^2) = 49π square inches
Now, let's calculate the cost per square inch for each pizza.
For the 12-inch pizza:
- Cost per square inch = $6.99/ (36π) square inches
For the 14-inch pizza:
- Cost per square inch = $7.99/ (49π) square inches
To determine which pizza offers a better value, divide the cost of each pizza by its respective area (in square inches).
For the 12-inch pizza:
- Cost = $6.99
- Area = 36π square inches
- Cost per square inch = $6.99 / (36π) ≈ $0.061 per square inch
For the 14-inch pizza:
- Cost = $7.99
- Area = 49π square inches
- Cost per square inch = $7.99 / (49π) ≈ $0.041 per square inch
Comparing the cost per square inch, the 14-inch pizza costs approximately $0.041 per square inch, while the 12-inch pizza costs approximately $0.061 per square inch.
Therefore, the larger 14-inch diameter pizza for $7.99 offers a better value in terms of cost per square inch compared to the 12-inch diameter pizza for $6.99.