To determine the order of the pizzas by the area of each slice from smallest to largest, follow these steps:
### Step-by-Step Calculation:
1. Calculate the Total Area of Each Pizza:
- Formula for the area of a circle: [tex]\( \text{Area} = \pi \times \text{radius}^2 \)[/tex].
2. Calculate the Area of Each Slice:
- Formula for the area of each slice: [tex]\( \text{Area of each slice} = \frac{\text{Total area}}{\text{Number of slices}} \)[/tex].
3. Compare the Areas of the Slices:
- Order the slices by comparing their areas.
#### Pizza 1:
- Radius: 16 inches
- Number of Slices: 8
1. Total area of Pizza 1:
[tex]\[
\text{Total area} = \pi \times 16^2 = 256\pi
\][/tex]
2. Area of each slice:
[tex]\[
\text{Area of each slice} = \frac{256\pi}{8} = 32\pi \approx 100.53 \, \text{sq inches}
\][/tex]
#### Pizza 2:
- Radius: 14 inches
- Number of Slices: 6
1. Total area of Pizza 2:
[tex]\[
\text{Total area} = \pi \times 14^2 = 196\pi
\][/tex]
2. Area of each slice:
[tex]\[
\text{Area of each slice} = \frac{196\pi}{6} \approx 32.67\pi \approx 102.63 \, \text{sq inches}
\][/tex]
#### Pizza 3:
- Radius: 12 inches
- Number of Slices: 4
1. Total area of Pizza 3:
[tex]\[
\text{Total area} = \pi \times 12^2 = 144\pi
\][/tex]
2. Area of each slice:
[tex]\[
\text{Area of each slice} = \frac{144\pi}{4} = 36\pi \approx 113.10 \, \text{sq inches}
\][/tex]
### Comparing the Areas:
[tex]\[
\begin{align*}
\text{Pizza 1 slice area} &\approx 100.53 \, \text{sq inches} \\
\text{Pizza 2 slice area} &\approx 102.63 \, \text{sq inches} \\
\text{Pizza 3 slice area} &\approx 113.10 \, \text{sq inches}
\end{align*}
\][/tex]
### Ordering from Smallest to Largest:
1. Slice from Pizza 1 (100.53 sq inches)
2. Slice from Pizza 2 (102.63 sq inches)
3. Slice from Pizza 3 (113.10 sq inches)
So, the table should be filled in as follows:
[tex]\[
\begin{tabular}{|c|}
\hline
Slice from Pizza 1 \\
\hline
Slice from Pizza 2 \\
\hline
Slice from Pizza 3 \\
\hline
\end{tabular}
\][/tex]
