To determine which pizza is a better deal based on price per square inch, we can calculate the area of each pizza and then divide the cost by the area.
First, let's calculate the area of each pizza using the formula for the area of a circle:
\[ \text{Area} = \pi r^2 \]
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4-inch radius pizza: \[ \text{Area} = \pi (4)^2 = \pi \cdot 16 \approx 50.27 \text{ square inches} \] Cost: $3 \[ \text{Price per square inch} = \frac{3}{50.27} \approx 0.0597 \text{ dollars per square inch} \]
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8-inch radius pizza: \[ \text{Area} = \pi (8)^2 = \pi \cdot 64 \approx 201.06 \text{ square inches} \] Cost: $14 \[ \text{Price per square inch} = \frac{14}{201.06} \approx 0.0695 \text{ dollars per square inch} \]
Now, comparing the prices per square inch:
- 4-inch pizza: approximately $0.0597 per square inch
- 8-inch pizza: approximately $0.0695 per square inch
Conclusion: The 4-inch radius pizza for $3 is the better deal, as it costs less per square inch than the 8-inch pizza for $14.