To determine which pizza option offers a better deal, we need to compare the area of the pizzas in each option since the price is the same for both offers.
1. Calculate the area of the pizzas:
The area \( A \) of a circle is calculated with 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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Radius of one medium pizza: \[ r = \frac{12}{2} = 6 \text{ inches} \]
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Area of one medium pizza: \[ A_{medium} = \pi (6^2) = \pi \times 36 = 36\pi \text{ square inches} \]
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Total area for 2 medium pizzas: \[ A_{total_medium} = 2 \times 36\pi = 72\pi \text{ square inches} \]
Option B: 1 Large Pizza (18" diameter)
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Radius of the large pizza: \[ r = \frac{18}{2} = 9 \text{ inches} \]
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Area of the large pizza: \[ A_{large} = \pi (9^2) = \pi \times 81 = 81\pi \text{ square inches} \]
2. Compare the total areas:
- Area of 2 medium pizzas (Option A): \( 72\pi \)
- Area of 1 large pizza (Option B): \( 81\pi \)
3. Conclusion:
To determine which option provides more pizza:
- Area of Option A: \( 72\pi \approx 226.08 \text{ square inches} \) (using \( \pi \approx 3.14 \))
- Area of Option B: \( 81\pi \approx 254.47 \text{ square inches} \)
Since \( 81\pi > 72\pi \), Option B (1 Large Pizza) provides a better deal as it has more pizza area for the same price.
Final Answer:
Option B (1 Large Pizza) is the better deal.
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