Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![**Problem: Find the Surface Area of My Bowling Ball**
**Given:**
- The diameter of the bowling ball is 8.5 inches.
### Explanation:
To calculate the surface area of a sphere (which is the shape of a bowling ball), we use the formula:
\[ \text{Surface Area} = 4 \pi r^2 \]
Where:
- \( r \) is the radius of the sphere.
- \( \pi \) (pi) is approximately 3.14159.
Given the diameter (8.5 inches), we first need to find the radius.
### Steps:
1. **Calculate the Radius**:
\[ r = \frac{\text{diameter}}{2} = \frac{8.5 \, \text{inches}}{2} = 4.25 \, \text{inches} \]
2. **Apply the Surface Area Formula**:
\[ \text{Surface Area} = 4 \pi (4.25)^2 \]
3. **Calculate**:
\[ \text{Surface Area} = 4 \pi (18.0625) \]
\[ \text{Surface Area} = 4 \times 3.14159 \times 18.0625 \]
\[ \text{Surface Area} \approx 227.032 \, \text{square inches} \]
**Answer: The surface area of the bowling ball is approximately 227.032 square inches.**
### Visual Representation:
The image shows a red bowling ball with three finger holes, typically used for gripping the ball during play. The ball appears smooth and spherical, matching the assumptions for the mathematical model described.
---
**Reference**: This problem helps reinforce the concept of surface area calculation for spheres, commonly encountered in geometry and everyday practical problems involving spherical objects.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff866d714-1042-4492-8e4c-16882ce6df0c%2F8549c19a-b258-4d27-8da6-ee4bbdcec5dd%2Fegv1vbs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Find the Surface Area of My Bowling Ball**
**Given:**
- The diameter of the bowling ball is 8.5 inches.
### Explanation:
To calculate the surface area of a sphere (which is the shape of a bowling ball), we use the formula:
\[ \text{Surface Area} = 4 \pi r^2 \]
Where:
- \( r \) is the radius of the sphere.
- \( \pi \) (pi) is approximately 3.14159.
Given the diameter (8.5 inches), we first need to find the radius.
### Steps:
1. **Calculate the Radius**:
\[ r = \frac{\text{diameter}}{2} = \frac{8.5 \, \text{inches}}{2} = 4.25 \, \text{inches} \]
2. **Apply the Surface Area Formula**:
\[ \text{Surface Area} = 4 \pi (4.25)^2 \]
3. **Calculate**:
\[ \text{Surface Area} = 4 \pi (18.0625) \]
\[ \text{Surface Area} = 4 \times 3.14159 \times 18.0625 \]
\[ \text{Surface Area} \approx 227.032 \, \text{square inches} \]
**Answer: The surface area of the bowling ball is approximately 227.032 square inches.**
### Visual Representation:
The image shows a red bowling ball with three finger holes, typically used for gripping the ball during play. The ball appears smooth and spherical, matching the assumptions for the mathematical model described.
---
**Reference**: This problem helps reinforce the concept of surface area calculation for spheres, commonly encountered in geometry and everyday practical problems involving spherical objects.
![# Calculating the Surface Area of a Soup Can
To find the surface area of this can of Progresso Garden Vegetables soup, let’s consider the can as a cylinder.
## Dimensions of the Can:
- **Height (h):** 4.5 inches
- **Radius (r):** 2 inches (diameter is given as 4 inches, hence the radius is half of the diameter)
The surface area (SA) of a cylinder is given by the formula:
\[ SA = 2\pi r (r + h) \]
where:
- \( \pi \) (pi) is approximately 3.14159
- \( r \) is the radius of the circular base
- \( h \) is the height of the cylinder
## Step-by-step Calculation:
1. **Calculate the lateral surface area:**
\[ \text{Lateral Surface Area} = 2\pi rh \]
\[ = 2 \times 3.14159 \times 2 \times 4.5 \]
\[ = 56.5487 \, \text{square inches} \]
2. **Calculate the area of the two circular bases:**
\[ \text{Total Area of Bases} = 2\pi r^2 \]
\[ = 2 \times 3.14159 \times 2^2 \]
\[ = 2 \times 3.14159 \times 4 \]
\[ = 25.13272 \, \text{square inches} \]
3. **Add the lateral surface area and the area of the bases:**
\[ SA = \text{Lateral Surface Area} + \text{Total Area of Bases} \]
\[ = 56.5487 + 25.13272 \]
\[ = 81.68142 \, \text{square inches} \]
Thus, the surface area of this can of soup is approximately **81.68 square inches.**
**Note:** The image used for the calculation shows a Progresso Garden Vegetables soup can with clear indications of the can’s height and diameter.
For additional questions on surface area and volume calculations, feel free to explore our other resources.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff866d714-1042-4492-8e4c-16882ce6df0c%2F8549c19a-b258-4d27-8da6-ee4bbdcec5dd%2Fs58he5d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Calculating the Surface Area of a Soup Can
To find the surface area of this can of Progresso Garden Vegetables soup, let’s consider the can as a cylinder.
## Dimensions of the Can:
- **Height (h):** 4.5 inches
- **Radius (r):** 2 inches (diameter is given as 4 inches, hence the radius is half of the diameter)
The surface area (SA) of a cylinder is given by the formula:
\[ SA = 2\pi r (r + h) \]
where:
- \( \pi \) (pi) is approximately 3.14159
- \( r \) is the radius of the circular base
- \( h \) is the height of the cylinder
## Step-by-step Calculation:
1. **Calculate the lateral surface area:**
\[ \text{Lateral Surface Area} = 2\pi rh \]
\[ = 2 \times 3.14159 \times 2 \times 4.5 \]
\[ = 56.5487 \, \text{square inches} \]
2. **Calculate the area of the two circular bases:**
\[ \text{Total Area of Bases} = 2\pi r^2 \]
\[ = 2 \times 3.14159 \times 2^2 \]
\[ = 2 \times 3.14159 \times 4 \]
\[ = 25.13272 \, \text{square inches} \]
3. **Add the lateral surface area and the area of the bases:**
\[ SA = \text{Lateral Surface Area} + \text{Total Area of Bases} \]
\[ = 56.5487 + 25.13272 \]
\[ = 81.68142 \, \text{square inches} \]
Thus, the surface area of this can of soup is approximately **81.68 square inches.**
**Note:** The image used for the calculation shows a Progresso Garden Vegetables soup can with clear indications of the can’s height and diameter.
For additional questions on surface area and volume calculations, feel free to explore our other resources.
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