### Composite Solid Volume Calculation #### Problem Statement: Find the volume of the composite solid. #### Diagram Explanation: The diagram shows a composite solid made up of two connected rectangular prisms. The dimensions are as follows: - The larger prism has a width of 12 feet, a length of 20 feet, and a height of 10 feet. - The smaller attached prism has a width of 12 feet, a length of 20 feet, and a height of 7 feet. The dimensions are labeled clearly on the diagram: - The 12 feet width is shown at the base. - The 20 feet length extends outwards. - Heights of 10 feet and 7 feet, respectively, are outlined for two different sections of the solid. #### Steps to Find the Volume: 1. **Calculate the volume of the larger rectangular prism:** \[ \text{Volume}_{\text{large}} = \text{Length} \times \text{Width} \times \text{Height} \] \[ \text{Volume}_{\text{large}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 10 \, \text{ft} \] \[ \text{Volume}_{\text{large}} = 2400 \, \text{ft}^3 \] 2. **Calculate the volume of the smaller rectangular prism:** \[ \text{Volume}_{\text{small}} = \text{Length} \times \text{Width} \times \text{Height} \] \[ \text{Volume}_{\text{small}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 7 \, \text{ft} \] \[ \text{Volume}_{\text{small}} = 1680 \, \text{ft}^3 \] 3. **Add the volumes of the two prisms to find the total volume:** \[ \text{Volume}_{\text{total}} = \text{Volume}_{\text{large}} + \text{Volume}_{\text{small}} \] \[ \text{Volume}_{\text{total}} = 2400 \, \text{ft}^3 + 1680 \, \text{ft}^3 \
### Composite Solid Volume Calculation #### Problem Statement: Find the volume of the composite solid. #### Diagram Explanation: The diagram shows a composite solid made up of two connected rectangular prisms. The dimensions are as follows: - The larger prism has a width of 12 feet, a length of 20 feet, and a height of 10 feet. - The smaller attached prism has a width of 12 feet, a length of 20 feet, and a height of 7 feet. The dimensions are labeled clearly on the diagram: - The 12 feet width is shown at the base. - The 20 feet length extends outwards. - Heights of 10 feet and 7 feet, respectively, are outlined for two different sections of the solid. #### Steps to Find the Volume: 1. **Calculate the volume of the larger rectangular prism:** \[ \text{Volume}_{\text{large}} = \text{Length} \times \text{Width} \times \text{Height} \] \[ \text{Volume}_{\text{large}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 10 \, \text{ft} \] \[ \text{Volume}_{\text{large}} = 2400 \, \text{ft}^3 \] 2. **Calculate the volume of the smaller rectangular prism:** \[ \text{Volume}_{\text{small}} = \text{Length} \times \text{Width} \times \text{Height} \] \[ \text{Volume}_{\text{small}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 7 \, \text{ft} \] \[ \text{Volume}_{\text{small}} = 1680 \, \text{ft}^3 \] 3. **Add the volumes of the two prisms to find the total volume:** \[ \text{Volume}_{\text{total}} = \text{Volume}_{\text{large}} + \text{Volume}_{\text{small}} \] \[ \text{Volume}_{\text{total}} = 2400 \, \text{ft}^3 + 1680 \, \text{ft}^3 \
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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![### Composite Solid Volume Calculation
#### Problem Statement:
Find the volume of the composite solid.
#### Diagram Explanation:
The diagram shows a composite solid made up of two connected rectangular prisms. The dimensions are as follows:
- The larger prism has a width of 12 feet, a length of 20 feet, and a height of 10 feet.
- The smaller attached prism has a width of 12 feet, a length of 20 feet, and a height of 7 feet.
The dimensions are labeled clearly on the diagram:
- The 12 feet width is shown at the base.
- The 20 feet length extends outwards.
- Heights of 10 feet and 7 feet, respectively, are outlined for two different sections of the solid.
#### Steps to Find the Volume:
1. **Calculate the volume of the larger rectangular prism:**
\[ \text{Volume}_{\text{large}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ \text{Volume}_{\text{large}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 10 \, \text{ft} \]
\[ \text{Volume}_{\text{large}} = 2400 \, \text{ft}^3 \]
2. **Calculate the volume of the smaller rectangular prism:**
\[ \text{Volume}_{\text{small}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ \text{Volume}_{\text{small}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 7 \, \text{ft} \]
\[ \text{Volume}_{\text{small}} = 1680 \, \text{ft}^3 \]
3. **Add the volumes of the two prisms to find the total volume:**
\[ \text{Volume}_{\text{total}} = \text{Volume}_{\text{large}} + \text{Volume}_{\text{small}} \]
\[ \text{Volume}_{\text{total}} = 2400 \, \text{ft}^3 + 1680 \, \text{ft}^3 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2323288b-18ff-4ac2-920b-0088f721212c%2Fe78a5e74-e3e1-49ad-887f-cbcd8dbae517%2Flcy48d.jpeg&w=3840&q=75)
Transcribed Image Text:### Composite Solid Volume Calculation
#### Problem Statement:
Find the volume of the composite solid.
#### Diagram Explanation:
The diagram shows a composite solid made up of two connected rectangular prisms. The dimensions are as follows:
- The larger prism has a width of 12 feet, a length of 20 feet, and a height of 10 feet.
- The smaller attached prism has a width of 12 feet, a length of 20 feet, and a height of 7 feet.
The dimensions are labeled clearly on the diagram:
- The 12 feet width is shown at the base.
- The 20 feet length extends outwards.
- Heights of 10 feet and 7 feet, respectively, are outlined for two different sections of the solid.
#### Steps to Find the Volume:
1. **Calculate the volume of the larger rectangular prism:**
\[ \text{Volume}_{\text{large}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ \text{Volume}_{\text{large}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 10 \, \text{ft} \]
\[ \text{Volume}_{\text{large}} = 2400 \, \text{ft}^3 \]
2. **Calculate the volume of the smaller rectangular prism:**
\[ \text{Volume}_{\text{small}} = \text{Length} \times \text{Width} \times \text{Height} \]
\[ \text{Volume}_{\text{small}} = 20 \, \text{ft} \times 12 \, \text{ft} \times 7 \, \text{ft} \]
\[ \text{Volume}_{\text{small}} = 1680 \, \text{ft}^3 \]
3. **Add the volumes of the two prisms to find the total volume:**
\[ \text{Volume}_{\text{total}} = \text{Volume}_{\text{large}} + \text{Volume}_{\text{small}} \]
\[ \text{Volume}_{\text{total}} = 2400 \, \text{ft}^3 + 1680 \, \text{ft}^3 \
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