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
find the volume of the composite solid . please round answer to the nearest hundredth
![**Find the volume of the composite solid. Round your answer to the nearest hundredth.**
The diagram shows a composite solid that consists of a cylindrical section. The dimensions are as follows:
- The length of the cylinder: 10 meters
- The radius of the cylinder: 2 meters
To find the volume of the cylindrical section, we use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \( r \) = radius of the cylinder
- \( h \) = height (or length) of the cylinder
Substitute the given values into the formula to find the volume:
\[ V = \pi (2\, m)^2 (10\, m) \]
\[ V = \pi (4\, m^2) (10\, m) \]
\[ V = 40\pi \, m^3 \]
Using the value of \( \pi \approx 3.14 \):
\[ V \approx 40 \times 3.14 \, m^3 \]
\[ V \approx 125.6 \, m^3 \]
Therefore, the volume of the composite solid, rounded to the nearest hundredth, is approximately:
\[ 125.60 \, m^3 \]
**Diagram Explanation:**
- The diagram shows a cylinder with a length (or height) of 10 meters.
- Each circle at the ends of the cylinder represents the cross-sectional area, with a radius of 2 meters clearly marked.
- The length of the cylinder is indicated by a horizontal line beneath the cylinder, labeled "10 m".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c5f49b-4667-4768-89ed-147e051dc540%2Fb70e86d8-d188-4ec4-916b-04cead1e285c%2F5a429n6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the volume of the composite solid. Round your answer to the nearest hundredth.**
The diagram shows a composite solid that consists of a cylindrical section. The dimensions are as follows:
- The length of the cylinder: 10 meters
- The radius of the cylinder: 2 meters
To find the volume of the cylindrical section, we use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \( r \) = radius of the cylinder
- \( h \) = height (or length) of the cylinder
Substitute the given values into the formula to find the volume:
\[ V = \pi (2\, m)^2 (10\, m) \]
\[ V = \pi (4\, m^2) (10\, m) \]
\[ V = 40\pi \, m^3 \]
Using the value of \( \pi \approx 3.14 \):
\[ V \approx 40 \times 3.14 \, m^3 \]
\[ V \approx 125.6 \, m^3 \]
Therefore, the volume of the composite solid, rounded to the nearest hundredth, is approximately:
\[ 125.60 \, m^3 \]
**Diagram Explanation:**
- The diagram shows a cylinder with a length (or height) of 10 meters.
- Each circle at the ends of the cylinder represents the cross-sectional area, with a radius of 2 meters clearly marked.
- The length of the cylinder is indicated by a horizontal line beneath the cylinder, labeled "10 m".
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning