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radius of cylinder = 5 cm radius of cone = 4 cm 12 cm 16 cm *

radius of cylinder = 5 cm radius of cone = 4 cm 12 cm 16 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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A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? when using  3.14 as an approximation of `pi`.

### Cylinder and Cone Dimensions In the diagram provided, we observe a cylinder and a cone. Here are the details and the measurements of both shapes: - **Cylinder**: - The cylinder is depicted with a blue outline. - It has a radius of **5 cm**. - The height of the cylinder is labeled as **16 cm**. - **Cone**: - The cone is shown inside the cylinder with a red outline. - It has a radius of **4 cm**. - The height of the cone is labeled as **12 cm**. ### Explanation of the Diagram - The cylinder and cone are both placed in such a way that their bases lie on the same plane. - The radius of the cylinder is larger than that of the cone. This can be seen as the cone is nested within the cylinder, and the difference in radii allows for the cone to fit inside without overlapping the cylinder's surface. - The heights of both shapes are marked with vertical double-headed arrows: - The outer arrow, spanning from the base to the top of the cylinder, indicates the full height of the cylinder, which is 16 cm. - The inner arrow, inside the cone, shows the height of the cone as 12 cm. These dimensions form the basis for various geometric calculations, such as finding the volume or surface area of these shapes, and are crucial in understanding the spatial relationships between them.
Transcribed Image Text:### Cylinder and Cone Dimensions In the diagram provided, we observe a cylinder and a cone. Here are the details and the measurements of both shapes: - **Cylinder**: - The cylinder is depicted with a blue outline. - It has a radius of **5 cm**. - The height of the cylinder is labeled as **16 cm**. - **Cone**: - The cone is shown inside the cylinder with a red outline. - It has a radius of **4 cm**. - The height of the cone is labeled as **12 cm**. ### Explanation of the Diagram - The cylinder and cone are both placed in such a way that their bases lie on the same plane. - The radius of the cylinder is larger than that of the cone. This can be seen as the cone is nested within the cylinder, and the difference in radii allows for the cone to fit inside without overlapping the cylinder's surface. - The heights of both shapes are marked with vertical double-headed arrows: - The outer arrow, spanning from the base to the top of the cylinder, indicates the full height of the cylinder, which is 16 cm. - The inner arrow, inside the cone, shows the height of the cone as 12 cm. These dimensions form the basis for various geometric calculations, such as finding the volume or surface area of these shapes, and are crucial in understanding the spatial relationships between them.
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