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What is the volume of the cylinder shown below? Leave your answer in terms of . 14 cm. 6 cm.

What is the volume of the cylinder shown below? Leave your answer in terms of . 14 cm. 6 cm.

Elementary Geometry For College Students, 7e
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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### Question 7 **What is the volume of the cylinder shown below? Leave your answer in terms of π.** ![Cylinder Diagram](path/to/image.jpg) 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:### Question 7 **What is the volume of the cylinder shown below? Leave your answer in terms of π.** ![Cylinder Diagram](path/to/image.jpg) 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 \( 504\pi \, \text{cm}^3 \).
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.
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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