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
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
![### Problem Statement
21. A cylinder has a diameter of 12 meters and a height of 12 meters. Find the volume. (use 3.14 for \(\pi\))
### Diagram
The problem is accompanied by a diagram of a cylinder. The cylinder's top circle and bottom circle are both labeled with a diameter of 12 meters, and the height of the cylinder is 12 meters.
### Multiple Choice Options
- A. 5425.92 m\(^3\)
- B. 1356.48 m\(^3\)
- C. 452.16 m\(^3\)
- D. 904.32 m\(^3\)
### Solution Explanation
To find the volume \(V\) of the cylinder, you use the formula:
\[ V = \pi r^2 h \]
Here:
- \( \pi \) is given as 3.14.
- \( r \) is the radius of the cylinder.
- \( h \) is the height of the cylinder.
Given the diameter is 12 meters, the radius \( r \) is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ meters} \]
The height \( h \) is 12 meters. Plugging the values into the volume formula, we get:
\[ V = 3.14 \times (6^2) \times 12 \]
\[ V = 3.14 \times 36 \times 12 \]
\[ V = 3.14 \times 432 \]
\[ V = 1356.48 \]
Hence, the correct volume is:
\[ 1356.48 \text{ m}^3 \]
So the correct answer is:
B. 1356.48 m\(^3\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5161d0-8c1c-4aef-9d6c-2e647d1b4222%2Faa80086e-9835-4d10-84ed-c2b5609a6ee4%2F5xfn9je_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
21. A cylinder has a diameter of 12 meters and a height of 12 meters. Find the volume. (use 3.14 for \(\pi\))
### Diagram
The problem is accompanied by a diagram of a cylinder. The cylinder's top circle and bottom circle are both labeled with a diameter of 12 meters, and the height of the cylinder is 12 meters.
### Multiple Choice Options
- A. 5425.92 m\(^3\)
- B. 1356.48 m\(^3\)
- C. 452.16 m\(^3\)
- D. 904.32 m\(^3\)
### Solution Explanation
To find the volume \(V\) of the cylinder, you use the formula:
\[ V = \pi r^2 h \]
Here:
- \( \pi \) is given as 3.14.
- \( r \) is the radius of the cylinder.
- \( h \) is the height of the cylinder.
Given the diameter is 12 meters, the radius \( r \) is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ meters} \]
The height \( h \) is 12 meters. Plugging the values into the volume formula, we get:
\[ V = 3.14 \times (6^2) \times 12 \]
\[ V = 3.14 \times 36 \times 12 \]
\[ V = 3.14 \times 432 \]
\[ V = 1356.48 \]
Hence, the correct volume is:
\[ 1356.48 \text{ m}^3 \]
So the correct answer is:
B. 1356.48 m\(^3\)
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