Question

which would result in more pizza? 1-12 inch pizza or 3-6 inch pizza. what's the area

Answer 1

To determine which option results in more pizza, we need to calculate the area of the pizzas in each scenario.

### 1. Area of the 12-inch pizza
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
For a 12-inch pizza:
- Diameter = 12 inches, so the radius \( r = \frac{12}{2} = 6 \) inches.
\[
A_{12} = \pi (6)^2 = 36\pi \quad \text{square inches}
\]

### 2. Area of the 3-6 inch pizzas
Each 6-inch pizza has a radius of:
- Diameter = 6 inches, so the radius \( r = \frac{6}{2} = 3 \) inches.
\[
A_{6} = \pi (3)^2 = 9\pi \quad \text{square inches}
\]

Since there are 3 of these pizzas:
\[
A_{3 \times 6} = 3 \times A_{6} = 3 \times 9\pi = 27\pi \quad \text{square inches}
\]

### Comparison
Now we can compare the areas:
- Area of 12-inch pizza = \( 36\pi \) square inches
- Total area of 3-6 inch pizzas = \( 27\pi \) square inches

### Conclusion
The 12-inch pizza has a larger area:
\[
36\pi > 27\pi
\]

Thus, a 12-inch pizza results in more pizza than 3 six-inch pizzas.