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24. How much larger is a pizza made in a 16-in square pizza pan than a pizza made in a 16-in diameter circular pan?

Ask by Moran Zimmerman. in the United States
Mar 20,2025

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The pizza made in the 16-inch square pan is \(64(4 - \pi)\) square inches larger than the pizza made in the 16-inch diameter circular pan.

Solución

1. **Determine the area of the square pizza.** Since the pan is a 16-inch square, each side has a length of \(16\) inches. The area of a square is given by \[ \text{Area}_{\text{square}} = (\text{side length})^2. \] Thus, \[ \text{Area}_{\text{square}} = 16^2 = 256\ \text{in}^2. \] 2. **Determine the area of the circular pizza.** The circular pan has a diameter of \(16\) inches, so its radius is \[ r = \frac{16}{2} = 8\ \text{inches}. \] The area of a circle is given by \[ \text{Area}_{\text{circle}} = \pi r^2. \] Thus, \[ \text{Area}_{\text{circle}} = \pi \times 8^2 = 64\pi\ \text{in}^2. \] 3. **Calculate how much larger the square pizza is compared to the circular pizza.** The difference in areas is \[ 256 - 64\pi\ \text{in}^2. \] Factoring out \(64\) gives \[ 64(4-\pi)\ \text{in}^2. \] 4. **Final Answer.** The pizza made in the 16-inch square pan is \(256 - 64\pi\) square inches larger than the pizza made in the 16-inch diameter circular pan, or equivalently, \(64(4-\pi)\) square inches larger.

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To find the area of the square pizza, you need to calculate \(16 \text{ in} \times 16 \text{ in} = 256 \text{ in}^2\). For the circular pizza, the area is found with the formula \(\pi r^2\) where the radius \(r = 8 \text{ in}\) (half of the 16-inch diameter), giving an area of \(\pi \times 8^2 \approx 201.06 \text{ in}^2\). Subtract the circular pizza area from the square pizza area: \(256 \text{ in}^2 - 201.06 \text{ in}^2 \approx 54.94 \text{ in}^2\). Therefore, the square pizza is roughly 54.94 square inches larger! So, when you're deciding between a square or a circular pizza, remember that those corners of the square give you extra deliciousness, adding up to almost 55 square inches more pizza goodness! Just think of all that extra cheesy goodness waiting to be devoured!

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