Question
Noah discovered that a 12-in.-diameter pizza costs $19.00. A 8-in.-diameter pizza costs $14.00. The 8-in.-diameter pizza is cut into six slices. The 12-in.-diameter pizza is cut into eight slices. Use 3.14 for pi.
Question content area bottom
Part 1
(a) What is the cost per slice of the 12-in.-diameter pizza?
$
2.38 (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 2
How many square inches of pizza are in one slice?
14.13 in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 3
(b) What is the cost per slice of the 8-in.-diameter pizza?
$
2.33 (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 4
How many square inches of pizza are in one slice?
8.37 in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 5
(c) If you want more value for your money, which slice of pizza should you buy?
8-in.-diameter pizza
12-in.-diameter pizza
Question content area bottom
Part 1
(a) What is the cost per slice of the 12-in.-diameter pizza?
$
2.38 (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 2
How many square inches of pizza are in one slice?
14.13 in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 3
(b) What is the cost per slice of the 8-in.-diameter pizza?
$
2.33 (Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 4
How many square inches of pizza are in one slice?
8.37 in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Part 5
(c) If you want more value for your money, which slice of pizza should you buy?
8-in.-diameter pizza
12-in.-diameter pizza
Answers
GPT-4o mini
To determine which pizza offers more value for your money, we need to calculate both the cost per square inch for each pizza (based on the area) and compare the two.
Let's break it down step by step:
### Step 1: Calculate the area of each pizza
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius.
#### For the 12-inch pizza:
- Diameter = 12 inches, so radius \( r = \frac{12}{2} = 6 \) inches.
\[
A_{12} = 3.14 \times (6^2) = 3.14 \times 36 = 113.04 \text{ square inches}
\]
#### For the 8-inch pizza:
- Diameter = 8 inches, so radius \( r = \frac{8}{2} = 4 \) inches.
\[
A_{8} = 3.14 \times (4^2) = 3.14 \times 16 = 50.24 \text{ square inches}
\]
### Step 2: Cost per square inch for each pizza
#### For the 12-inch pizza:
- Cost = $19.00
\[
\text{Cost per square inch}_{12} = \frac{19}{113.04} \approx 0.168 \text{ dollars per square inch}
\]
#### For the 8-inch pizza:
- Cost = $14.00
\[
\text{Cost per square inch}_{8} = \frac{14}{50.24} \approx 0.278 \text{ dollars per square inch}
\]
### Step 3: Conclusion
Now we compare the cost per square inch. The 12-inch pizza costs approximately $0.168 per square inch, while the 8-inch pizza costs approximately $0.278 per square inch.
### Answer:
(c) If you want more value for your money, **you should buy the 12-inch-diameter pizza.**
Let's break it down step by step:
### Step 1: Calculate the area of each pizza
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius.
#### For the 12-inch pizza:
- Diameter = 12 inches, so radius \( r = \frac{12}{2} = 6 \) inches.
\[
A_{12} = 3.14 \times (6^2) = 3.14 \times 36 = 113.04 \text{ square inches}
\]
#### For the 8-inch pizza:
- Diameter = 8 inches, so radius \( r = \frac{8}{2} = 4 \) inches.
\[
A_{8} = 3.14 \times (4^2) = 3.14 \times 16 = 50.24 \text{ square inches}
\]
### Step 2: Cost per square inch for each pizza
#### For the 12-inch pizza:
- Cost = $19.00
\[
\text{Cost per square inch}_{12} = \frac{19}{113.04} \approx 0.168 \text{ dollars per square inch}
\]
#### For the 8-inch pizza:
- Cost = $14.00
\[
\text{Cost per square inch}_{8} = \frac{14}{50.24} \approx 0.278 \text{ dollars per square inch}
\]
### Step 3: Conclusion
Now we compare the cost per square inch. The 12-inch pizza costs approximately $0.168 per square inch, while the 8-inch pizza costs approximately $0.278 per square inch.
### Answer:
(c) If you want more value for your money, **you should buy the 12-inch-diameter pizza.**