Elementary Geometry For College Students, 7e
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ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Using 3.14, what is the length of the cylinder rounded to the nearest whole number?
![### Problem 7: Cylindrical Mailing Tube Problem
A cylindrical mailing tube has a volume of 311 cubic inches and a diameter of 6 inches.
Using \(\pi = 3.14\), what is the length of the cylinder rounded to the nearest whole number?
**Options:**
- A) 3
- B) 10
- C) 11
- D) 33
#### Explanation:
To solve for the length of the cylinder, we use the volume formula for a cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height (or length in this context),
- \(\pi \) is approximately equal to 3.14.
Given:
- \( V = 311 \) cubic inches,
- Diameter = 6 inches, hence the radius \( r = \frac{Diameter}{2} = \frac{6}{2} = 3 \) inches.
Substituting the known values into the formula:
\[ 311 = 3.14 \times 3^2 \times h \]
\[ 311 = 3.14 \times 9 \times h \]
\[ 311 = 28.26 \times h \]
\[ h \approx \frac{311}{28.26} \]
\[ h \approx 11 \]
Therefore, the length of the cylinder is approximately 11 inches.
**Answer: C) 11**](https://content.bartleby.com/qna-images/question/d85d7dbc-14f9-4467-8305-4d38df6f0396/8a672d1c-9ead-4201-b38f-0d8e36e1e22a/rnrtuu_processed.jpeg)
Transcribed Image Text:### Problem 7: Cylindrical Mailing Tube Problem
A cylindrical mailing tube has a volume of 311 cubic inches and a diameter of 6 inches.
Using \(\pi = 3.14\), what is the length of the cylinder rounded to the nearest whole number?
**Options:**
- A) 3
- B) 10
- C) 11
- D) 33
#### Explanation:
To solve for the length of the cylinder, we use the volume formula for a cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height (or length in this context),
- \(\pi \) is approximately equal to 3.14.
Given:
- \( V = 311 \) cubic inches,
- Diameter = 6 inches, hence the radius \( r = \frac{Diameter}{2} = \frac{6}{2} = 3 \) inches.
Substituting the known values into the formula:
\[ 311 = 3.14 \times 3^2 \times h \]
\[ 311 = 3.14 \times 9 \times h \]
\[ 311 = 28.26 \times h \]
\[ h \approx \frac{311}{28.26} \]
\[ h \approx 11 \]
Therefore, the length of the cylinder is approximately 11 inches.
**Answer: C) 11**
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