Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 14A
Related questions
Question
The diagram of the cylinder provides two key measurements:
- The radius of the cylinder's base is **6 cm**.
- The height (or length) of the cylinder is **14 cm**.
To find the volume of the cylinder, we use the formula:
\[ \text{Volume} = \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
By substituting the given values into the formula:
\[ \text{Volume} = \pi (6 \, \text{cm})^2 (14 \, \text{cm}) \]
\[ \text{Volume} = \pi (36 \, \text{cm}^2) (14 \, \text{cm}) \]
\[ \text{Volume} = 504 \pi \, \text{cm}^3 \]
Thus, the volume of the cylinder is \( 504\pi \, \text{cm}^3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01db270a-c525-4661-be5b-2b24ecb0478b%2Fbbdeea6d-8b17-4aa9-aac5-4ac63ea3fccc%2F2pfqg9c_processed.png&w=3840&q=75)
Transcribed Image Text:### Question 7
**What is the volume of the cylinder shown below? Leave your answer in terms of π.**
The diagram of the cylinder provides two key measurements:
- The radius of the cylinder's base is **6 cm**.
- The height (or length) of the cylinder is **14 cm**.
To find the volume of the cylinder, we use the formula:
\[ \text{Volume} = \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
By substituting the given values into the formula:
\[ \text{Volume} = \pi (6 \, \text{cm})^2 (14 \, \text{cm}) \]
\[ \text{Volume} = \pi (36 \, \text{cm}^2) (14 \, \text{cm}) \]
\[ \text{Volume} = 504 \pi \, \text{cm}^3 \]
Thus, the volume of the cylinder is \( 504\pi \, \text{cm}^3 \).
Transcribed Image Text:The image shown represents a multiple-choice question, likely related to mathematics or geometry focusing on volume calculations. Here are the choices presented:
A. \( 504\pi \, \text{cm}^3 \)
B. \( 84\pi \, \text{cm}^3 \)
C. \( 156\pi \, \text{cm}^3 \)
D. \( 126\pi \, \text{cm}^3 \)
Each option is accompanied by an empty checkbox next to it, indicating that the user should select the correct answer from the list.
This format is typical in educational quizzes or assessments, where an understanding of the formulas for the volume of solids (such as spheres, cylinders, or cones) involving the mathematical constant \(\pi\) may be tested.
No graphs or diagrams are present in this image.
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