To determine the areas of the slices for each pizza and then order them from the smallest area to the largest area, we follow these steps:
1. Calculate the area of each pizza:
- The area of a circle is given by [tex]\( \pi \times \text{radius}^2 \)[/tex].
For Pizza 1:
- Radius: 16 inches
- Area: [tex]\( \pi \times (16)^2 \)[/tex]
- Area: [tex]\( 804.247 \)[/tex] square inches
For Pizza 2:
- Radius: 14 inches
- Area: [tex]\( \pi \times (14)^2 \)[/tex]
- Area: [tex]\( 615.752 \)[/tex] square inches
For Pizza 3:
- Radius: 12 inches
- Area: [tex]\( \pi \times (12)^2 \)[/tex]
- Area: [tex]\( 452.389 \)[/tex] square inches
2. Calculate the area of each slice:
- The area of one slice = Total area of pizza / Number of slices
For Pizza 1:
- Number of slices: 8
- Area per slice: [tex]\( \frac{804.247}{8} = 100.530 \)[/tex] square inches
For Pizza 2:
- Number of slices: 6
- Area per slice: [tex]\( \frac{615.752}{6} = 102.625 \)[/tex] square inches
For Pizza 3:
- Number of slices: 4
- Area per slice: [tex]\( \frac{452.389}{4} = 113.097 \)[/tex] square inches
3. Order the areas of the slices from smallest to largest:
- Slice from Pizza 1: [tex]\( 100.530 \)[/tex] square inches
- Slice from Pizza 2: [tex]\( 102.625 \)[/tex] square inches
- Slice from Pizza 3: [tex]\( 113.097 \)[/tex] square inches
So, putting the pizzas in order by the area of a slice from smallest to largest:
[tex]\[
\text{slice from Pizza 1} \quad \rightarrow \quad \text{slice from Pizza 2} \quad \rightarrow \quad \text{slice from Pizza 3}
\][/tex]
