**Problem Statement:** The volume of a cylindrical can is \(32\pi \, \text{in}^3\). If the height of the can is 2 inches, what is its radius, in inches? **Options:** - \(2 \, \text{in}\) - \(4 \, \text{in}\) - \(8 \, \text{in}\) - \(16 \, \text{in}\) **Explanation:** To find the radius of the cylindrical 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. Given: - \( V = 32\pi \, \text{in}^3 \) - \( h = 2 \, \text{in} \) Replace the known values into the formula: \[ 32\pi = \pi r^2 \times 2 \] Divide both sides by \(\pi\): \[ 32 = 2r^2 \] Then divide by 2: \[ 16 = r^2 \] Take the square root of both sides: \[ r = 4 \, \text{in} \] Therefore, the radius of the cylindrical can is \(4 \, \text{in}\).
**Problem Statement:** The volume of a cylindrical can is \(32\pi \, \text{in}^3\). If the height of the can is 2 inches, what is its radius, in inches? **Options:** - \(2 \, \text{in}\) - \(4 \, \text{in}\) - \(8 \, \text{in}\) - \(16 \, \text{in}\) **Explanation:** To find the radius of the cylindrical 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. Given: - \( V = 32\pi \, \text{in}^3 \) - \( h = 2 \, \text{in} \) Replace the known values into the formula: \[ 32\pi = \pi r^2 \times 2 \] Divide both sides by \(\pi\): \[ 32 = 2r^2 \] Then divide by 2: \[ 16 = r^2 \] Take the square root of both sides: \[ r = 4 \, \text{in} \] Therefore, the radius of the cylindrical can is \(4 \, \text{in}\).
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
Related questions
Question
![**Problem Statement:**
The volume of a cylindrical can is \(32\pi \, \text{in}^3\). If the height of the can is 2 inches, what is its radius, in inches?
**Options:**
- \(2 \, \text{in}\)
- \(4 \, \text{in}\)
- \(8 \, \text{in}\)
- \(16 \, \text{in}\)
**Explanation:**
To find the radius of the cylindrical 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.
Given:
- \( V = 32\pi \, \text{in}^3 \)
- \( h = 2 \, \text{in} \)
Replace the known values into the formula:
\[ 32\pi = \pi r^2 \times 2 \]
Divide both sides by \(\pi\):
\[ 32 = 2r^2 \]
Then divide by 2:
\[ 16 = r^2 \]
Take the square root of both sides:
\[ r = 4 \, \text{in} \]
Therefore, the radius of the cylindrical can is \(4 \, \text{in}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40ac1924-da82-497b-85f4-398551157699%2Fc91bad4f-1dd4-4bcb-a5e9-221d081b8f8a%2Fy8l988i.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The volume of a cylindrical can is \(32\pi \, \text{in}^3\). If the height of the can is 2 inches, what is its radius, in inches?
**Options:**
- \(2 \, \text{in}\)
- \(4 \, \text{in}\)
- \(8 \, \text{in}\)
- \(16 \, \text{in}\)
**Explanation:**
To find the radius of the cylindrical 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.
Given:
- \( V = 32\pi \, \text{in}^3 \)
- \( h = 2 \, \text{in} \)
Replace the known values into the formula:
\[ 32\pi = \pi r^2 \times 2 \]
Divide both sides by \(\pi\):
\[ 32 = 2r^2 \]
Then divide by 2:
\[ 16 = r^2 \]
Take the square root of both sides:
\[ r = 4 \, \text{in} \]
Therefore, the radius of the cylindrical can is \(4 \, \text{in}\).
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