Question
PART B:
#8-#10
Find Surface area and Volume of the following 3D shapes. Show all your work.
8.)
A.) Arrange the steps for finding Surface Area (3 points) and solve (2 points):
Step 1: Click Here
Step 2: Click Here
SOLVE:
Surface Area =__________
B.) Arrange the steps for finding Volume (3 points) and solve (2 points):
Step 1: Click Here
Step 2: Click Here
SOLVE:
Volume =__________
PART B:
#8-#10
Find Surface area and Volume of the following 3D shapes. Show all your work.
8.)
A.) Arrange the steps for finding Surface Area (3 points) and solve (2 points):
Step 1: Click Here
Step 2: Click Here
SOLVE:
Surface Area =__________
B.) Arrange the steps for finding Volume (3 points) and solve (2 points):
Step 1: Click Here
Step 2: Click Here
SOLVE:
Volume =__________
Answers
Answered by
GPT-4o mini
To answer your request, I will assume we are calculating the surface area and volume of a specific solid shape, such as a cylinder. Below is a structured response with steps, calculations, and answers for both surface area and volume.
### **3D Shape: Cylinder**
**Given:**
- Radius (r): 5 cm
- Height (h): 10 cm
### **A.) Surface Area Calculation**
#### **Steps to Find Surface Area:**
1. **Calculate the area of the two circular bases.**
- Formula: \( A_{base} = \pi r^2 \)
2. **Calculate the lateral surface area of the cylinder.**
- Formula: \( A_{lateral} = 2\pi rh \)
3. **Add the areas of the bases and the lateral area to find total surface area.**
- Formula: \( A_{total} = 2A_{base} + A_{lateral} \)
**SOLVING:**
1. Calculate the area of the bases:
\[
A_{base} = \pi (5^2) = \pi \times 25 = 25\pi \approx 78.54 \, \text{cm}^2
\]
(since \( \pi \approx 3.14 \))
2. Calculate lateral surface area:
\[
A_{lateral} = 2\pi (5)(10) = 100\pi \approx 314.16 \, \text{cm}^2
\]
3. Calculate total surface area:
\[
A_{total} = 2(25\pi) + 100\pi = 50\pi + 100\pi = 150\pi \approx 471.24 \, \text{cm}^2
\]
### **Surface Area = 471.24 cm²**
---
### **B.) Volume Calculation**
#### **Steps to Find Volume:**
1. **Calculate the volume using the formula for the volume of a cylinder.**
- Formula: \( V = \pi r^2 h \)
**SOLVING:**
1. Calculate the volume:
\[
V = \pi (5^2)(10) = \pi \times 25 \times 10 = 250\pi \approx 785.40 \, \text{cm}^3
\]
### **Volume = 785.40 cm³**
---
You can apply this same structured approach for other shapes (like spheres, cubes, or cones) by using their respective formulas and following similar steps. If you have a specific shape in mind for questions 9 and 10, please let me know!
### **3D Shape: Cylinder**
**Given:**
- Radius (r): 5 cm
- Height (h): 10 cm
### **A.) Surface Area Calculation**
#### **Steps to Find Surface Area:**
1. **Calculate the area of the two circular bases.**
- Formula: \( A_{base} = \pi r^2 \)
2. **Calculate the lateral surface area of the cylinder.**
- Formula: \( A_{lateral} = 2\pi rh \)
3. **Add the areas of the bases and the lateral area to find total surface area.**
- Formula: \( A_{total} = 2A_{base} + A_{lateral} \)
**SOLVING:**
1. Calculate the area of the bases:
\[
A_{base} = \pi (5^2) = \pi \times 25 = 25\pi \approx 78.54 \, \text{cm}^2
\]
(since \( \pi \approx 3.14 \))
2. Calculate lateral surface area:
\[
A_{lateral} = 2\pi (5)(10) = 100\pi \approx 314.16 \, \text{cm}^2
\]
3. Calculate total surface area:
\[
A_{total} = 2(25\pi) + 100\pi = 50\pi + 100\pi = 150\pi \approx 471.24 \, \text{cm}^2
\]
### **Surface Area = 471.24 cm²**
---
### **B.) Volume Calculation**
#### **Steps to Find Volume:**
1. **Calculate the volume using the formula for the volume of a cylinder.**
- Formula: \( V = \pi r^2 h \)
**SOLVING:**
1. Calculate the volume:
\[
V = \pi (5^2)(10) = \pi \times 25 \times 10 = 250\pi \approx 785.40 \, \text{cm}^3
\]
### **Volume = 785.40 cm³**
---
You can apply this same structured approach for other shapes (like spheres, cubes, or cones) by using their respective formulas and following similar steps. If you have a specific shape in mind for questions 9 and 10, please let me know!