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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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.
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![### Question 2
**What is the volume of the empty tube in the middle?** Round your answer to the nearest tenth. Do not include the units.
#### Diagram Description:
The diagram shows a large cylinder with a smaller, green-shaded, central cylinder inside it. The dimensions are as follows:
- The height of both cylinders is 4 ft.
- The radius of the larger cylinder is 3 ft.
- The radius of the smaller (green) cylinder is 2 ft.
The task is to calculate the volume of the smaller cylinder.
To find the volume \( V \) of a cylinder, you use the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius
- \( h \) is the height
For the smaller cylinder:
- \( r = 2 \) ft
- \( h = 4 \) ft
Substitute these values into the formula:
\[ V = \pi (2)^2 (4) \]
\[ V = \pi (4) (4) \]
\[ V = 16\pi \]
Calculating \( 16\pi \approx 16 \times 3.14 = 50.24 \)
So, the volume of the empty tube in the middle is approximately \( 50.2 \) cubic feet when rounded to the nearest tenth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F323d6556-21e9-45dc-8903-2418fedb39d6%2Fe2d6f4bd-9d0e-4492-b96f-2b485610ae4d%2Fb2ys1p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 2
**What is the volume of the empty tube in the middle?** Round your answer to the nearest tenth. Do not include the units.
#### Diagram Description:
The diagram shows a large cylinder with a smaller, green-shaded, central cylinder inside it. The dimensions are as follows:
- The height of both cylinders is 4 ft.
- The radius of the larger cylinder is 3 ft.
- The radius of the smaller (green) cylinder is 2 ft.
The task is to calculate the volume of the smaller cylinder.
To find the volume \( V \) of a cylinder, you use the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius
- \( h \) is the height
For the smaller cylinder:
- \( r = 2 \) ft
- \( h = 4 \) ft
Substitute these values into the formula:
\[ V = \pi (2)^2 (4) \]
\[ V = \pi (4) (4) \]
\[ V = 16\pi \]
Calculating \( 16\pi \approx 16 \times 3.14 = 50.24 \)
So, the volume of the empty tube in the middle is approximately \( 50.2 \) cubic feet when rounded to the nearest tenth.
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