A cylindrical mailing tube has a volume of 311 cubic inches and a diameter of 6 inches. Using T 3.14, what is the length of the cylinder rounded to the nearest whole number? A 3 B 10 11 D 33
A cylindrical mailing tube has a volume of 311 cubic inches and a diameter of 6 inches. Using T 3.14, what is the length of the cylinder rounded to the nearest whole number? A 3 B 10 11 D 33
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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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
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**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd85d7dbc-14f9-4467-8305-4d38df6f0396%2F8a672d1c-9ead-4201-b38f-0d8e36e1e22a%2Frnrtuu_processed.jpeg&w=3840&q=75)
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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