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
find the volume of the right cylinder
- The cylinder has a height (\(h\)) of 5 meters.
- The radius (\(r\)) of the base of the cylinder is 3 meters.
#### Solution
To find the volume (\(V\)) of a right cylinder, use the formula:
\[ V = \pi r^2 h \]
Given:
\[ r = 3 \, \text{m} \]
\[ h = 5 \, \text{m} \]
Substitute the values into the formula:
\[ V = \pi (3)^2 (5) \]
\[ V = \pi (9) (5) \]
\[ V = 45 \pi \]
Using \(\pi \approx 3.14159\):
\[ V \approx 45 \times 3.14159 \]
\[ V \approx 141.47 \]
Therefore, the volume of the cylinder is approximately **141.47 cubic meters (m³)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e9d242-cb37-4bc8-a74f-f7cca1efbc15%2F351070b4-5d9a-4c67-b69d-b7d0cb8fa904%2Fbk9q5gr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Volume of a Right Cylinder
**Objective**: Find the volume of the right cylinder.
**Instructions**: Do not type units. Round to the nearest hundredth.
#### Problem Description
1. You are given a right cylinder with the following dimensions:
- Radius (\(r\)): 3 meters
- Height (\(h\)): 5 meters
#### Diagram Description
The diagram below shows a right cylinder:
- The cylinder has a height (\(h\)) of 5 meters.
- The radius (\(r\)) of the base of the cylinder is 3 meters.
#### Solution
To find the volume (\(V\)) of a right cylinder, use the formula:
\[ V = \pi r^2 h \]
Given:
\[ r = 3 \, \text{m} \]
\[ h = 5 \, \text{m} \]
Substitute the values into the formula:
\[ V = \pi (3)^2 (5) \]
\[ V = \pi (9) (5) \]
\[ V = 45 \pi \]
Using \(\pi \approx 3.14159\):
\[ V \approx 45 \times 3.14159 \]
\[ V \approx 141.47 \]
Therefore, the volume of the cylinder is approximately **141.47 cubic meters (m³)**.
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