To determine which pizza option offers the best deal, we need to calculate the total area of each option since the price is the same for both. The pizza with a larger total area will provide more pizza at the same price.
The area \( A \) of a circle is calculated using the formula:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.
Option A: 2 Medium Pizzas (12" diameter)
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Calculate the radius of a medium pizza:
- Diameter = 12 inches
- Radius \( r = \frac{Diameter}{2} = \frac{12}{2} = 6 \) inches
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Calculate the area of one medium pizza:
\[ A_{medium} = \pi (6^2) = \pi (36) \approx 113.10 \text{ square inches} \]
- Calculate the total area for 2 medium pizzas:
\[ A_{total, medium} = 2 \times A_{medium} = 2 \times 113.10 \approx 226.20 \text{ square inches} \]
Option B: 1 Large Pizza (18" diameter)
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Calculate the radius of a large pizza:
- Diameter = 18 inches
- Radius \( r = \frac{Diameter}{2} = \frac{18}{2} = 9 \) inches
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Calculate the area of the large pizza:
\[ A_{large} = \pi (9^2) = \pi (81) \approx 254.47 \text{ square inches} \]
Conclusion
- Total area for 2 medium pizzas: \( \approx 226.20 \text{ square inches} \)
- Total area for 1 large pizza: \( \approx 254.47 \text{ square inches} \)
Since \( 254.47 \) square inches (option B) is greater than \( 226.20 \) square inches (option A), Option B (1 Large Pizza) provides the best deal in terms of pizza area for the price.
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