What is the volume of the cylinder shown below? Volume cylinder = r²h diameter r= 14 cm. 0 Your response should show all necessary calculations and diagrams. 6 cm. 0
What is the volume of the cylinder shown below? Volume cylinder = r²h diameter r= 14 cm. 0 Your response should show all necessary calculations and diagrams. 6 cm. 0
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
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![### Understanding the Volume of a Cylinder
**Question:** What is the volume of the cylinder shown below?
**Volume Formula:**
\[ \text{Volume}_{\text{cylinder}} = \pi r^2 h \]
**Where:**
- \( r = \frac{\text{diameter}}{2} \)
### Given Measurements:
- **Diameter:** 6 cm
- **Height (h):** 14 cm
### Steps to Calculate the Volume:
1. **Determine the radius (r):**
\[
r = \frac{\text{diameter}}{2} = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm}
\]
2. **Substitute the radius and height into the volume formula:**
\[
\text{Volume}_{\text{cylinder}} = \pi r^2 h = \pi (3 \, \text{cm})^2 (14 \, \text{cm})
\]
3. **Calculate \( r^2 \):**
\[
r^2 = (3 \, \text{cm})^2 = 9 \, \text{cm}^2
\]
4. **Calculate the volume:**
\[
\text{Volume}_{\text{cylinder}} = \pi \times 9 \, \text{cm}^2 \times 14 \, \text{cm} = 126\pi \, \text{cm}^3
\]
5. **Approximate the volume (using \(\pi \approx 3.14159\)):**
\[
\text{Volume}_{\text{cylinder}} \approx 126 \times 3.14159 \, \text{cm}^3 \approx 396.06 \, \text{cm}^3
\]
### Diagram Explanation:
- The diagram presents a cylinder with a diameter of 6 cm and a height of 14 cm.
- The radius has been calculated from the given diameter.
- The height is the length of the cylinder.
This example demonstrates how to determine the volume of a cylinder using given diameter and height measurements and applying the formula \( \pi r^2 h \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95b555fe-c61f-4380-ac77-d5f60f2cc03d%2F1f510813-5647-42e1-b67c-d97527b37e4b%2Fagk361v_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Volume of a Cylinder
**Question:** What is the volume of the cylinder shown below?
**Volume Formula:**
\[ \text{Volume}_{\text{cylinder}} = \pi r^2 h \]
**Where:**
- \( r = \frac{\text{diameter}}{2} \)
### Given Measurements:
- **Diameter:** 6 cm
- **Height (h):** 14 cm
### Steps to Calculate the Volume:
1. **Determine the radius (r):**
\[
r = \frac{\text{diameter}}{2} = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm}
\]
2. **Substitute the radius and height into the volume formula:**
\[
\text{Volume}_{\text{cylinder}} = \pi r^2 h = \pi (3 \, \text{cm})^2 (14 \, \text{cm})
\]
3. **Calculate \( r^2 \):**
\[
r^2 = (3 \, \text{cm})^2 = 9 \, \text{cm}^2
\]
4. **Calculate the volume:**
\[
\text{Volume}_{\text{cylinder}} = \pi \times 9 \, \text{cm}^2 \times 14 \, \text{cm} = 126\pi \, \text{cm}^3
\]
5. **Approximate the volume (using \(\pi \approx 3.14159\)):**
\[
\text{Volume}_{\text{cylinder}} \approx 126 \times 3.14159 \, \text{cm}^3 \approx 396.06 \, \text{cm}^3
\]
### Diagram Explanation:
- The diagram presents a cylinder with a diameter of 6 cm and a height of 14 cm.
- The radius has been calculated from the given diameter.
- The height is the length of the cylinder.
This example demonstrates how to determine the volume of a cylinder using given diameter and height measurements and applying the formula \( \pi r^2 h \).
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