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
![### Determining the Volume of Various Figures
Use the formulas \( V = \pi r^2 h \) for cylinders and \( V = l \times w \times h \) for rectangular prisms to find the volume. For \(\pi\), use 3.14, and round your answer to the nearest whole number.
**Figure 1: Cylinder**
- **Description**: A 3D diagram of a cylinder is shown.
- **Dimensions**:
- Height (\( h \)): 7 km
- Diameter: 8 km (thus, radius \( r = 4 \) km)
- **Volume Calculation**:
\[
V = \pi r^2 h = 3.14 \times 4^2 \times 7
\]
Simplifying:
\[
V = 3.14 \times 16 \times 7 = 3.14 \times 112 = 351.68 \text{ km}^3
\]
Rounded to the nearest whole number:
\[
V \approx 352 \text{ km}^3
\]
- **Recorded Volume**: 56 km\(^3\)
**Figure 2: Rectangular Prism**
- **Description**: A 3D diagram of a rectangular prism (box) is depicted.
- **Dimensions**:
- Length (\( l \)): 6 cm
- Width (\( w \)): 5 cm
- Height (\( h \)): 7 cm
- **Volume Calculation**:
\[
V = l \times w \times h = 6 \times 5 \times 7 = 210 \text{ cm}^3
\]
Rounded to the nearest whole number:
\[
V \approx 210 \text{ cm}^3
\]
- **Recorded Volume**: 175 cm\(^3\)
**Explanation of Errors**: The correct calculations should reveal that the volume of the cylinder should be approximately 352 km\(^3\), not 56 km\(^3\), and the volume of the rectangular prism should be 210 cm\(^3\), not 175 cm\(^3\). Measurements may have been miscalculated or incorrectly inputted in the provided answer boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa242a625-2826-4f00-ad8f-039422d3d327%2F471f650c-a0c9-48d1-ba4d-7d7c012ee835%2Fzbtqiwk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determining the Volume of Various Figures
Use the formulas \( V = \pi r^2 h \) for cylinders and \( V = l \times w \times h \) for rectangular prisms to find the volume. For \(\pi\), use 3.14, and round your answer to the nearest whole number.
**Figure 1: Cylinder**
- **Description**: A 3D diagram of a cylinder is shown.
- **Dimensions**:
- Height (\( h \)): 7 km
- Diameter: 8 km (thus, radius \( r = 4 \) km)
- **Volume Calculation**:
\[
V = \pi r^2 h = 3.14 \times 4^2 \times 7
\]
Simplifying:
\[
V = 3.14 \times 16 \times 7 = 3.14 \times 112 = 351.68 \text{ km}^3
\]
Rounded to the nearest whole number:
\[
V \approx 352 \text{ km}^3
\]
- **Recorded Volume**: 56 km\(^3\)
**Figure 2: Rectangular Prism**
- **Description**: A 3D diagram of a rectangular prism (box) is depicted.
- **Dimensions**:
- Length (\( l \)): 6 cm
- Width (\( w \)): 5 cm
- Height (\( h \)): 7 cm
- **Volume Calculation**:
\[
V = l \times w \times h = 6 \times 5 \times 7 = 210 \text{ cm}^3
\]
Rounded to the nearest whole number:
\[
V \approx 210 \text{ cm}^3
\]
- **Recorded Volume**: 175 cm\(^3\)
**Explanation of Errors**: The correct calculations should reveal that the volume of the cylinder should be approximately 352 km\(^3\), not 56 km\(^3\), and the volume of the rectangular prism should be 210 cm\(^3\), not 175 cm\(^3\). Measurements may have been miscalculated or incorrectly inputted in the provided answer boxes.
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