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?
enter your response here in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
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?
enter your response here in. squared
(Type a whole number or a decimal rounded to the nearest hundredth as needed.)
Answers
GPT-4o mini
To solve the problems in parts 1-4, we will calculate the relevant values step-by-step.
### Part 1 (a)
**Cost per slice of the 12-in.-diameter pizza:**
1. **Total Cost:** $19.00
2. **Number of Slices:** 8
**Cost per Slice:**
\[
\text{Cost per slice} = \frac{\text{Total Cost}}{\text{Number of Slices}} = \frac{19.00}{8} = 2.375
\]
Rounded to the nearest hundredth:
\[
\text{Cost per slice} = \$2.38
\]
### Part 2
**How many square inches of pizza are in one slice of the 12-in.-diameter pizza:**
1. **Radius of the pizza:** Diameter / 2 = 12 in / 2 = 6 in
2. **Area of the pizza:**
\[
\text{Area} = \pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ in.}^2
\]
3. **Area per slice:**
\[
\text{Area per slice} = \frac{\text{Total Area}}{\text{Number of Slices}} = \frac{113.04}{8} = 14.13 \text{ in.}^2
\]
### Part 3 (b)
**Cost per slice of the 8-in.-diameter pizza:**
1. **Total Cost:** $14.00
2. **Number of Slices:** 6
**Cost per Slice:**
\[
\text{Cost per slice} = \frac{\text{Total Cost}}{\text{Number of Slices}} = \frac{14.00}{6} \approx 2.3333
\]
Rounded to the nearest hundredth:
\[
\text{Cost per slice} = \$2.33
\]
### Part 4
**How many square inches of pizza are in one slice of the 8-in.-diameter pizza:**
1. **Radius of the pizza:** Diameter / 2 = 8 in / 2 = 4 in
2. **Area of the pizza:**
\[
\text{Area} = \pi r^2 = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ in.}^2
\]
3. **Area per slice:**
\[
\text{Area per slice} = \frac{\text{Total Area}}{\text{Number of Slices}} = \frac{50.24}{6} \approx 8.3733
\]
Rounded to the nearest hundredth:
\[
\text{Area per slice} = 8.37 \text{ in.}^2
\]
### Final Answers
1. Part 1: Cost per slice of the 12-in.-diameter pizza = **$2.38**
2. Part 2: Area in one slice of the 12-in.-diameter pizza = **14.13 in.²**
3. Part 3: Cost per slice of the 8-in.-diameter pizza = **$2.33**
4. Part 4: Area in one slice of the 8-in.-diameter pizza = **8.37 in.²**
### Part 1 (a)
**Cost per slice of the 12-in.-diameter pizza:**
1. **Total Cost:** $19.00
2. **Number of Slices:** 8
**Cost per Slice:**
\[
\text{Cost per slice} = \frac{\text{Total Cost}}{\text{Number of Slices}} = \frac{19.00}{8} = 2.375
\]
Rounded to the nearest hundredth:
\[
\text{Cost per slice} = \$2.38
\]
### Part 2
**How many square inches of pizza are in one slice of the 12-in.-diameter pizza:**
1. **Radius of the pizza:** Diameter / 2 = 12 in / 2 = 6 in
2. **Area of the pizza:**
\[
\text{Area} = \pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36 = 113.04 \text{ in.}^2
\]
3. **Area per slice:**
\[
\text{Area per slice} = \frac{\text{Total Area}}{\text{Number of Slices}} = \frac{113.04}{8} = 14.13 \text{ in.}^2
\]
### Part 3 (b)
**Cost per slice of the 8-in.-diameter pizza:**
1. **Total Cost:** $14.00
2. **Number of Slices:** 6
**Cost per Slice:**
\[
\text{Cost per slice} = \frac{\text{Total Cost}}{\text{Number of Slices}} = \frac{14.00}{6} \approx 2.3333
\]
Rounded to the nearest hundredth:
\[
\text{Cost per slice} = \$2.33
\]
### Part 4
**How many square inches of pizza are in one slice of the 8-in.-diameter pizza:**
1. **Radius of the pizza:** Diameter / 2 = 8 in / 2 = 4 in
2. **Area of the pizza:**
\[
\text{Area} = \pi r^2 = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ in.}^2
\]
3. **Area per slice:**
\[
\text{Area per slice} = \frac{\text{Total Area}}{\text{Number of Slices}} = \frac{50.24}{6} \approx 8.3733
\]
Rounded to the nearest hundredth:
\[
\text{Area per slice} = 8.37 \text{ in.}^2
\]
### Final Answers
1. Part 1: Cost per slice of the 12-in.-diameter pizza = **$2.38**
2. Part 2: Area in one slice of the 12-in.-diameter pizza = **14.13 in.²**
3. Part 3: Cost per slice of the 8-in.-diameter pizza = **$2.33**
4. Part 4: Area in one slice of the 8-in.-diameter pizza = **8.37 in.²**