To determine the order of the pizzas by the area of each slice from smallest to largest, we need to calculate the area of each slice for the given pizzas.
For Pizza 1:
- Radius = 16 inches
- Number of slices = 8
- The area of the entire pizza can be found using the formula for the area of a circle, [tex]\( A = \pi r^2 \)[/tex]:
[tex]\[ A_1 = \pi \times 16^2 = \pi \times 256 = 804.247 \text{ square inches} \][/tex]
- Since the pizza is cut into 8 slices, the area of one slice is:
[tex]\[ \frac{804.247}{8} = 100.531 \text{ square inches} \][/tex]
For Pizza 2:
- Radius = 14 inches
- Number of slices = 6
- The area of the entire pizza is:
[tex]\[ A_2 = \pi \times 14^2 = \pi \times 196 = 615.752 \text{ square inches} \][/tex]
- Since the pizza is cut into 6 slices, the area of one slice is:
[tex]\[ \frac{615.752}{6} = 102.625 \text{ square inches} \][/tex]
For Pizza 3:
- Radius = 12 inches
- Number of slices = 4
- The area of the entire pizza is:
[tex]\[ A_3 = \pi \times 12^2 = \pi \times 144 = 452.389 \text{ square inches} \][/tex]
- Since the pizza is cut into 4 slices, the area of one slice is:
[tex]\[ \frac{452.389}{4} = 113.097 \text{ square inches} \][/tex]
Now, we can order the slices from smallest to largest by their areas:
1. Slice from Pizza 1: [tex]\(100.531 \text{ square inches}\)[/tex]
2. Slice from Pizza 2: [tex]\(102.625 \text{ square inches}\)[/tex]
3. Slice from Pizza 3: [tex]\(113.097 \text{ square inches}\)[/tex]
So, the pizzas in order by the area of a slice from smallest area to largest area are:
[tex]\[
\text{slice from pizza 1} \quad \square
\][/tex]
[tex]\[
\text{slice from pizza 2} \quad \square
\][/tex]
[tex]\[
\text{slice from pizza 3} \quad \square
\][/tex]
