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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![### Volume Calculation of a Cylindrical Solid
#### Problem Statement
**Question 12:** Find the volume of the solid to the nearest whole cubic unit. Use a calculator, if needed.
A cylindrical solid is illustrated with the following dimensions:
- Radius (r): 2.45 cm
- Height (h): 12.3 cm
The options for the volume of the cylinder are given as:
- 232 cm³
- 224 cm³
- 242 cm³
- 212 cm³
#### Solution
To find the volume (V) of a cylinder, use the formula:
\[ V = \pi r^2 h \]
where:
- \( \pi \) (Pi) is approximately 3.14159
- \( r \) is the radius of the base
- \( h \) is the height of the cylinder
Let's calculate:
1. **Square the radius**:
\[ r^2 = (2.45 \, \text{cm})^2 = 6.0025 \, \text{cm}^2 \]
2. **Multiply by the height**:
\[ r^2 \times h = 6.0025 \, \text{cm}^2 \times 12.3 \, \text{cm} = 73.23175 \, \text{cm}^3 \]
3. **Multiply by \( \pi \)**:
\[ V = \pi \times 73.23175 \, \text{cm}^3 = 3.14159 \times 73.23175 \, \text{cm}^3 \approx 229.938 \, \text{cm}^3 \]
4. **Round to the nearest whole cubic unit**:
\[ V \approx 230 \, \text{cm}^3 \]
However, since 230 cm³ is not one of the provided options, there may be a slight misunderstanding in the precision of the given choices. Let's quickly verify the closest provided option:
- 242 cm³
Given the calculation, 242 cm³ is quite off from our computed value of 230 cm³. The closest option to the computed value could be an approximation related to another decimal place calculation.
Considering precision and educational purposes, if following the exact given process strictly:
**Volume**:
\[ V = \pi](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f1b5800-f045-4ccc-a00d-a1a031eae7ac%2Fa1bcde35-527a-4a0b-91e7-698acd0314b8%2Fo618ujo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Volume Calculation of a Cylindrical Solid
#### Problem Statement
**Question 12:** Find the volume of the solid to the nearest whole cubic unit. Use a calculator, if needed.
A cylindrical solid is illustrated with the following dimensions:
- Radius (r): 2.45 cm
- Height (h): 12.3 cm
The options for the volume of the cylinder are given as:
- 232 cm³
- 224 cm³
- 242 cm³
- 212 cm³
#### Solution
To find the volume (V) of a cylinder, use the formula:
\[ V = \pi r^2 h \]
where:
- \( \pi \) (Pi) is approximately 3.14159
- \( r \) is the radius of the base
- \( h \) is the height of the cylinder
Let's calculate:
1. **Square the radius**:
\[ r^2 = (2.45 \, \text{cm})^2 = 6.0025 \, \text{cm}^2 \]
2. **Multiply by the height**:
\[ r^2 \times h = 6.0025 \, \text{cm}^2 \times 12.3 \, \text{cm} = 73.23175 \, \text{cm}^3 \]
3. **Multiply by \( \pi \)**:
\[ V = \pi \times 73.23175 \, \text{cm}^3 = 3.14159 \times 73.23175 \, \text{cm}^3 \approx 229.938 \, \text{cm}^3 \]
4. **Round to the nearest whole cubic unit**:
\[ V \approx 230 \, \text{cm}^3 \]
However, since 230 cm³ is not one of the provided options, there may be a slight misunderstanding in the precision of the given choices. Let's quickly verify the closest provided option:
- 242 cm³
Given the calculation, 242 cm³ is quite off from our computed value of 230 cm³. The closest option to the computed value could be an approximation related to another decimal place calculation.
Considering precision and educational purposes, if following the exact given process strictly:
**Volume**:
\[ V = \pi
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