Answer :
Certainly! Let's break down the problem step-by-step:
### Step 1: Understanding the Problem
You have three different pizzas with varying radii and different numbers of slices. You need to compare the area of one slice from each pizza and order them from smallest to largest.
### Step 2: Given Data
We are provided with the following:
- Pizza 1: Radius = 16 inches, Slices = 8
- Pizza 2: Radius = 14 inches, Slices = 6
- Pizza 3: Radius = 12 inches, Slices = 4
### Step 3: Formula for Area of a Circle
The area [tex]\( A \)[/tex] of a circle is calculated using the formula:
[tex]\[ A = \pi \times r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
### Step 4: Calculate the Total Area of Each Pizza
- Pizza 1:
[tex]\[ A_1 = \pi \times 16^2 = \pi \times 256 \][/tex]
- Pizza 2:
[tex]\[ A_2 = \pi \times 14^2 = \pi \times 196 \][/tex]
- Pizza 3:
[tex]\[ A_3 = \pi \times 12^2 = \pi \times 144 \][/tex]
### Step 5: Calculate the Area of One Slice from Each Pizza
For each pizza, we divide the total area by the number of slices.
- Slice from Pizza 1:
[tex]\[ \text{Area of each slice} = \frac{\pi \times 256}{8} = \pi \times 32 \][/tex]
- Slice from Pizza 2:
[tex]\[ \text{Area of each slice} = \frac{\pi \times 196}{6} \approx \pi \times 32.6667 \][/tex]
- Slice from Pizza 3:
[tex]\[ \text{Area of each slice} = \frac{\pi \times 144}{4} = \pi \times 36 \][/tex]
### Step 6: Numerical Results
Notice that:
- [tex]\(\pi \times 32 \approx 100.53 \)[/tex] (Area of a slice from Pizza 1)
- [tex]\(\pi \times 32.6667 \approx 102.63 \)[/tex] (Area of a slice from Pizza 2)
- [tex]\(\pi \times 36 \approx 113.10 \)[/tex] (Area of a slice from Pizza 3)
### Step 7: Ordering the Slices
Now we order the area of the slices from smallest to largest:
[tex]\[ 100.53 \ (\text{Pizza 1}) \ < \ 102.63 \ (\text{Pizza 2}) \ < \ 113.10 \ (\text{Pizza 3}) \][/tex]
### Step 8: Conclusion
Thus, the order of slices from smallest to largest area is:
- Slice from pizza 1
- Slice from pizza 2
- Slice from pizza 3
So, the correct ordering is:
[tex]\[ \text{Slice from pizza 1} \ < \ \text{Slice from pizza 2} \ < \ \text{Slice from pizza 3} \][/tex]
### Step 1: Understanding the Problem
You have three different pizzas with varying radii and different numbers of slices. You need to compare the area of one slice from each pizza and order them from smallest to largest.
### Step 2: Given Data
We are provided with the following:
- Pizza 1: Radius = 16 inches, Slices = 8
- Pizza 2: Radius = 14 inches, Slices = 6
- Pizza 3: Radius = 12 inches, Slices = 4
### Step 3: Formula for Area of a Circle
The area [tex]\( A \)[/tex] of a circle is calculated using the formula:
[tex]\[ A = \pi \times r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
### Step 4: Calculate the Total Area of Each Pizza
- Pizza 1:
[tex]\[ A_1 = \pi \times 16^2 = \pi \times 256 \][/tex]
- Pizza 2:
[tex]\[ A_2 = \pi \times 14^2 = \pi \times 196 \][/tex]
- Pizza 3:
[tex]\[ A_3 = \pi \times 12^2 = \pi \times 144 \][/tex]
### Step 5: Calculate the Area of One Slice from Each Pizza
For each pizza, we divide the total area by the number of slices.
- Slice from Pizza 1:
[tex]\[ \text{Area of each slice} = \frac{\pi \times 256}{8} = \pi \times 32 \][/tex]
- Slice from Pizza 2:
[tex]\[ \text{Area of each slice} = \frac{\pi \times 196}{6} \approx \pi \times 32.6667 \][/tex]
- Slice from Pizza 3:
[tex]\[ \text{Area of each slice} = \frac{\pi \times 144}{4} = \pi \times 36 \][/tex]
### Step 6: Numerical Results
Notice that:
- [tex]\(\pi \times 32 \approx 100.53 \)[/tex] (Area of a slice from Pizza 1)
- [tex]\(\pi \times 32.6667 \approx 102.63 \)[/tex] (Area of a slice from Pizza 2)
- [tex]\(\pi \times 36 \approx 113.10 \)[/tex] (Area of a slice from Pizza 3)
### Step 7: Ordering the Slices
Now we order the area of the slices from smallest to largest:
[tex]\[ 100.53 \ (\text{Pizza 1}) \ < \ 102.63 \ (\text{Pizza 2}) \ < \ 113.10 \ (\text{Pizza 3}) \][/tex]
### Step 8: Conclusion
Thus, the order of slices from smallest to largest area is:
- Slice from pizza 1
- Slice from pizza 2
- Slice from pizza 3
So, the correct ordering is:
[tex]\[ \text{Slice from pizza 1} \ < \ \text{Slice from pizza 2} \ < \ \text{Slice from pizza 3} \][/tex]
