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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Find the height of a cylinder with a radius of 35 m and a volume of 19250 m^3
![Here is the transcription of the given content with detailed explanations suitable for an educational website:
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### Question 8
**Find the height of a cylinder with a radius of \(35 \, m\) and a volume of \(19250 \, m^3\).**
**Use \(\pi = 3.14\).**
Options:
- **A)** \(5 \, m\)
- **B)** \(15 \, m\)
- **C)** \(20 \, m\)
- **D)** \(175 \, m\)
#### Explanation:
To solve for the height \(h\) of the cylinder, we can use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
Where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height,
- \(\pi\) is pi (a constant approximately equal to 3.14).
Given:
- Volume (\(V\)) = \(19250 \, m^3\)
- Radius (\(r\)) = \(35 \, m\)
- \(\pi\) = 3.14
We need to find the height \(h\).
First, rearrange the formula to solve for \(h\):
\[
h = \frac{V}{\pi r^2}
\]
Substitute the given values into the equation:
\[
h = \frac{19250}{3.14 \times (35)^2}
\]
Calculate \(35^2\):
\[
35^2 = 1225
\]
Now calculate \(3.14 \times 1225\):
\[
3.14 \times 1225 = 3846.5
\]
Finally, divide \(19250\) by \(3846.5\):
\[
h = \frac{19250}{3846.5} \approx 5 \, m
\]
Hence, the height of the cylinder is:
**Answer:** \(A\) \(5 \, m\)
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd85d7dbc-14f9-4467-8305-4d38df6f0396%2Fbb870302-6e45-442f-a5c9-9b1ba548fc57%2Fp0v5wn9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Here is the transcription of the given content with detailed explanations suitable for an educational website:
---
### Question 8
**Find the height of a cylinder with a radius of \(35 \, m\) and a volume of \(19250 \, m^3\).**
**Use \(\pi = 3.14\).**
Options:
- **A)** \(5 \, m\)
- **B)** \(15 \, m\)
- **C)** \(20 \, m\)
- **D)** \(175 \, m\)
#### Explanation:
To solve for the height \(h\) of the cylinder, we can use the formula for the volume of a cylinder:
\[
V = \pi r^2 h
\]
Where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height,
- \(\pi\) is pi (a constant approximately equal to 3.14).
Given:
- Volume (\(V\)) = \(19250 \, m^3\)
- Radius (\(r\)) = \(35 \, m\)
- \(\pi\) = 3.14
We need to find the height \(h\).
First, rearrange the formula to solve for \(h\):
\[
h = \frac{V}{\pi r^2}
\]
Substitute the given values into the equation:
\[
h = \frac{19250}{3.14 \times (35)^2}
\]
Calculate \(35^2\):
\[
35^2 = 1225
\]
Now calculate \(3.14 \times 1225\):
\[
3.14 \times 1225 = 3846.5
\]
Finally, divide \(19250\) by \(3846.5\):
\[
h = \frac{19250}{3846.5} \approx 5 \, m
\]
Hence, the height of the cylinder is:
**Answer:** \(A\) \(5 \, m\)
---
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