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
number 13 (9.3)
![### Example Problem: Volume of an Oblique Circular Cylinder
#### Problem 13:
**Task:** Find the volume of the oblique circular cylinder. The axis meets the plane of the base to form a 45° angle.
- **Given:**
- Radius \( r = 2 \) inches
- Height \( h = 8\frac{1}{2} \) inches (or 8.5 inches)
**Solution:**
1. **Identify the Cylinder Type:**
- This is an oblique cylinder, meaning the sides are not perpendicular to the bases.
2. **Formula for Volume of a Cylinder:**
- The formula for the volume \( V \) of any cylinder is \( V = \pi r^2 h \).
3. **Apply Given Values:**
- Substitute \( r = 2 \) and \( h = 8.5 \):
\[
V = \pi (2)^2 (8.5)
\]
\[
V = \pi (4)(8.5)
\]
\[
V = \pi (34)
\]
4. **Calculate the Volume:**
- If needed, use the value of \( \pi \approx 3.14159 \) for a numerical answer:
\[
V \approx 3.14159 \times 34 \approx 106.81 \text{ cubic inches}
\]
**Answer:**
- The volume of the oblique circular cylinder is approximately \( 106.81 \) cubic inches.
##### Diagram Description:
- The image contains a diagram of a cylinder with the following dimensions indicated:
- Radius \( r = 2 \) inches
- Height \( h = 8.5 \) inches
- The cylinder is depicted as oblique with the longitudinal axis forming a 45° angle with the base.
This explanation includes the necessary steps and calculations for determining the volume of an oblique circular cylinder.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F945b10b0-0c22-48ad-878e-6ed5d406b626%2Feac80913-9c09-4dee-a6d5-3855b34d4e81%2Fcrr44s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem: Volume of an Oblique Circular Cylinder
#### Problem 13:
**Task:** Find the volume of the oblique circular cylinder. The axis meets the plane of the base to form a 45° angle.
- **Given:**
- Radius \( r = 2 \) inches
- Height \( h = 8\frac{1}{2} \) inches (or 8.5 inches)
**Solution:**
1. **Identify the Cylinder Type:**
- This is an oblique cylinder, meaning the sides are not perpendicular to the bases.
2. **Formula for Volume of a Cylinder:**
- The formula for the volume \( V \) of any cylinder is \( V = \pi r^2 h \).
3. **Apply Given Values:**
- Substitute \( r = 2 \) and \( h = 8.5 \):
\[
V = \pi (2)^2 (8.5)
\]
\[
V = \pi (4)(8.5)
\]
\[
V = \pi (34)
\]
4. **Calculate the Volume:**
- If needed, use the value of \( \pi \approx 3.14159 \) for a numerical answer:
\[
V \approx 3.14159 \times 34 \approx 106.81 \text{ cubic inches}
\]
**Answer:**
- The volume of the oblique circular cylinder is approximately \( 106.81 \) cubic inches.
##### Diagram Description:
- The image contains a diagram of a cylinder with the following dimensions indicated:
- Radius \( r = 2 \) inches
- Height \( h = 8.5 \) inches
- The cylinder is depicted as oblique with the longitudinal axis forming a 45° angle with the base.
This explanation includes the necessary steps and calculations for determining the volume of an oblique circular cylinder.
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