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
![**Transcription for Educational Website: Calculating the Volume of a Cylindrical Battery**
---
### Objective:
To find the **volume** of this battery.
### Battery Dimensions:
- **Diameter (d):** 25 mm.
- **Height (h):** 47 mm.
### Diagram Explanation:
Displayed is a cylindrical battery with labeled measurements:
1. **Diameter** (represented by the pink dashed lines at the top): Measured as 25 mm.
2. **Height** (represented by the pink dashed lines at the side): Measured as 47 mm.
### Calculating the Volume:
To find the volume of a cylinder, use the formula:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume.
- \( r \) is the radius (half of the diameter).
- \( h \) is the height.
- \( \pi \) (Pi) is a constant approximately equal to 3.14159.
### Steps:
1. Find the radius of the battery:
\[
r = \frac{d}{2} = \frac{25 \text{ mm}}{2} = 12.5 \text{ mm}
\]
2. Substitute the radius and height into the volume formula:
\[
V = \pi (12.5 \text{ mm})^2 (47 \text{ mm})
\]
\[
V = \pi (156.25 \text{ mm}^2) (47 \text{ mm})
\]
\[
V = \pi \times 7343.75 \text{ mm}^3
\]
\[
V \approx 3.14159 \times 7343.75 \text{ mm}^3
\]
\[
V \approx 23086.61 \text{ mm}^3
\]
### Conclusion:
The volume of the given battery is approximately **23086.61 cubic millimeters (mm³)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6723c038-ec47-4bfd-80a5-b112ac1b61f2%2Ffc23a9ea-bcc0-4c91-b80f-9660016649c4%2Fthn53dh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website: Calculating the Volume of a Cylindrical Battery**
---
### Objective:
To find the **volume** of this battery.
### Battery Dimensions:
- **Diameter (d):** 25 mm.
- **Height (h):** 47 mm.
### Diagram Explanation:
Displayed is a cylindrical battery with labeled measurements:
1. **Diameter** (represented by the pink dashed lines at the top): Measured as 25 mm.
2. **Height** (represented by the pink dashed lines at the side): Measured as 47 mm.
### Calculating the Volume:
To find the volume of a cylinder, use the formula:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume.
- \( r \) is the radius (half of the diameter).
- \( h \) is the height.
- \( \pi \) (Pi) is a constant approximately equal to 3.14159.
### Steps:
1. Find the radius of the battery:
\[
r = \frac{d}{2} = \frac{25 \text{ mm}}{2} = 12.5 \text{ mm}
\]
2. Substitute the radius and height into the volume formula:
\[
V = \pi (12.5 \text{ mm})^2 (47 \text{ mm})
\]
\[
V = \pi (156.25 \text{ mm}^2) (47 \text{ mm})
\]
\[
V = \pi \times 7343.75 \text{ mm}^3
\]
\[
V \approx 3.14159 \times 7343.75 \text{ mm}^3
\]
\[
V \approx 23086.61 \text{ mm}^3
\]
### Conclusion:
The volume of the given battery is approximately **23086.61 cubic millimeters (mm³)**.
![### Understanding the Volume of a Sphere: A Practical Example with a Basketball
To find the volume of a sphere, such as a basketball, we can use the following formula:
\[ V = \frac{4}{3} \pi r^3 \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the sphere,
- \( \pi \) (pi) is approximately 3.14159.
#### Example Problem
**Given**: The radius of the basketball is 4.75 inches.
**Find**: The volume of the basketball.
### Step-by-Step Solution
1. **Identify the given value**:
\[ r = 4.75 \, \text{inches} \]
2. **Plug the given radius into the volume formula**:
\[ V = \frac{4}{3} \pi (4.75)^3 \]
3. **Calculate the radius cubed**:
\[ (4.75)^3 = 107.171875 \]
4. **Multiply by pi**:
\[ \pi \times 107.171875 \approx 336.574 \]
5. **Finish the calculation by multiplying by \( \frac{4}{3} \)**:
\[ V = \frac{4}{3} \times 336.574 \]
\[ V \approx 448.763 \, \text{cubic inches} \]
Therefore, the volume of the basketball is approximately 448.763 cubic inches.
#### Visual Representation
The image provided shows a standard basketball, characterized by its orange color and black seams. For practical exercises, this visual can help students understand the context of applying the sphere volume formula to real-world objects.
### Conclusion
Using the sphere volume formula, students can calculate the volume of spherical objects like basketballs, enhancing their comprehension of geometric principles and their applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6723c038-ec47-4bfd-80a5-b112ac1b61f2%2Ffc23a9ea-bcc0-4c91-b80f-9660016649c4%2Ftm8l87l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Volume of a Sphere: A Practical Example with a Basketball
To find the volume of a sphere, such as a basketball, we can use the following formula:
\[ V = \frac{4}{3} \pi r^3 \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the sphere,
- \( \pi \) (pi) is approximately 3.14159.
#### Example Problem
**Given**: The radius of the basketball is 4.75 inches.
**Find**: The volume of the basketball.
### Step-by-Step Solution
1. **Identify the given value**:
\[ r = 4.75 \, \text{inches} \]
2. **Plug the given radius into the volume formula**:
\[ V = \frac{4}{3} \pi (4.75)^3 \]
3. **Calculate the radius cubed**:
\[ (4.75)^3 = 107.171875 \]
4. **Multiply by pi**:
\[ \pi \times 107.171875 \approx 336.574 \]
5. **Finish the calculation by multiplying by \( \frac{4}{3} \)**:
\[ V = \frac{4}{3} \times 336.574 \]
\[ V \approx 448.763 \, \text{cubic inches} \]
Therefore, the volume of the basketball is approximately 448.763 cubic inches.
#### Visual Representation
The image provided shows a standard basketball, characterized by its orange color and black seams. For practical exercises, this visual can help students understand the context of applying the sphere volume formula to real-world objects.
### Conclusion
Using the sphere volume formula, students can calculate the volume of spherical objects like basketballs, enhancing their comprehension of geometric principles and their applications.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning