Which one of the following is a better buy: a large pizza with a 12
-inch
diameter for $ 15.00
or a medium pizza with a 6
-inch
diameter for $ 5.00
?
To compare the two options, we need to calculate the price per square inch of pizza.
For the large pizza:
- Radius is half the diameter, so the radius of this pizza is 6 inches.
- Area of a circle = πr², so the area of this pizza is π(6)² = 36π square inches.
- Price per square inch = $15.00 ÷ 36π ≈ $0.13/square inch.
For the medium pizza:
- Radius is half the diameter, so the radius of this pizza is 3 inches.
- Area of a circle = πr², so the area of this pizza is π(3)² = 9π square inches.
- Price per square inch = $5.00 ÷ 9π ≈ $0.18/square inch.
Therefore, the large pizza is the better buy, since it has a lower price per square inch of pizza.
To determine which pizza is a better buy, we need to compare the prices per square inch of each pizza.
Step 1: Calculate the area of each pizza:
- Large pizza: The area of a circle can be calculated using the formula A = π * r^2, where r is the radius. Since the diameter of the large pizza is 12 inches, the radius is half of that, which is 6 inches. Therefore, the area of the large pizza is A = π * (6^2) = 36π square inches.
- Medium pizza: Again, using the same formula, the area of the medium pizza is A = π * (3^2) = 9π square inches.
Step 2: Calculate the price per square inch:
- Large pizza: The price of the large pizza is $15.00, so the price per square inch is $15.00 / (36π square inches).
- Medium pizza: The price of the medium pizza is $5.00, so the price per square inch is $5.00 / (9π square inches).
Step 3: Simplify the expressions for better comparison:
- Large pizza: The price per square inch of the large pizza is approximately $0.1324 / square inch.
- Medium pizza: The price per square inch of the medium pizza is approximately $0.1763 / square inch.
Step 4: Compare the prices per square inch:
Comparing the prices per square inch, we can see that the large pizza is more cost-effective since it has a lower price per square inch ($0.1324/square inch) compared to the medium pizza ($0.1763/square inch).
Therefore, the large pizza with a 12-inch diameter for $15.00 is a better buy.