Find the volume of a cylinder with a base area of 257T and height equal to the radius. Give your answer in terms of T . A 25T B 156.37 C 125T D 6257
Find the volume of a cylinder with a base area of 257T and height equal to the radius. Give your answer in terms of T . A 25T B 156.37 C 125T D 6257
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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20. Find the volume of a cylinder with a base area of 25π and the higher equal to the radius. Give you answer in terms of π
![### Cylinder Volume Calculation Question
#### Question 20/36
**Problem Statement:**
*Find the volume of a cylinder with a base area of \( 25\pi \) and height equal to the radius. Give your answer in terms of \(\pi\).*
**Answer Choices:**
- A) \( 25\pi \)
- B) \( 156.3\pi \)
- C) \( 125\pi \)
- D) \( 625\pi \)
#### Explanation:
To solve this problem, we need to use the formula for the volume of a cylinder, which is given by:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
Given that the base area (\( A \)) of the cylinder is \( 25\pi \), we know:
\[ A = \pi r^2 = 25\pi \]
From this, we can isolate \( r \):
\[ r^2 = 25 \]
\[ r = \sqrt{25} \]
\[ r = 5 \]
Since the height \( h \) is given to be equal to the radius \( r \), \( h = 5 \).
Now, we can plug the values of \( r \) and \( h \) back into the volume formula:
\[ V = \pi r^2 h \]
\[ V = \pi (5^2) (5) \]
\[ V = \pi (25) (5) \]
\[ V = 125\pi \]
So, the correct answer is:
- C) \( 125\pi \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34bff1e1-af68-4229-b0ef-aa0aaa134e46%2F8adda647-0745-4f00-9edf-ef66e3cbdb69%2Fmu0nxgk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Cylinder Volume Calculation Question
#### Question 20/36
**Problem Statement:**
*Find the volume of a cylinder with a base area of \( 25\pi \) and height equal to the radius. Give your answer in terms of \(\pi\).*
**Answer Choices:**
- A) \( 25\pi \)
- B) \( 156.3\pi \)
- C) \( 125\pi \)
- D) \( 625\pi \)
#### Explanation:
To solve this problem, we need to use the formula for the volume of a cylinder, which is given by:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
Given that the base area (\( A \)) of the cylinder is \( 25\pi \), we know:
\[ A = \pi r^2 = 25\pi \]
From this, we can isolate \( r \):
\[ r^2 = 25 \]
\[ r = \sqrt{25} \]
\[ r = 5 \]
Since the height \( h \) is given to be equal to the radius \( r \), \( h = 5 \).
Now, we can plug the values of \( r \) and \( h \) back into the volume formula:
\[ V = \pi r^2 h \]
\[ V = \pi (5^2) (5) \]
\[ V = \pi (25) (5) \]
\[ V = 125\pi \]
So, the correct answer is:
- C) \( 125\pi \)
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