3. A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft. What is the volume, in cubic feet, of space the tent occupies? 13 ft 9 ft 8 ft -8 ft- CONTEMPLATE CALCULATE
3. A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft. What is the volume, in cubic feet, of space the tent occupies? 13 ft 9 ft 8 ft -8 ft- CONTEMPLATE CALCULATE
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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![### Geometry Problem: Calculating the Volume of a Vendor's Tent
**Problem Statement:**
A vendor is using an 8 ft by 8 ft tent for a craft fair. The legs of the tent are 9 ft tall, and the top forms a square pyramid with a height of 3 ft.
**Question:**
What is the volume, in cubic feet, of space the tent occupies?
**Diagram Explanation:**
The diagram illustrates a tent composed of two parts:
1. **A rectangular base (prism)** - The base dimensions are 8 feet by 8 feet, and it has a height of 9 feet.
2. **A square pyramid on top** - The base of this pyramid coincides with the top of the rectangular prism, and it has a height of 3 feet.
**Dimensions:**
- Base of the tent: 8 ft x 8 ft
- Height of the rectangular part: 9 ft
- Height of the pyramid: 3 ft
**Steps to Calculate the Volume:**
1. **Volume of the rectangular base:**
\[ V_{\text{rectangular}} = \text{length} \times \text{width} \times \text{height} \]
\[ V_{\text{rectangular}} = 8\ \text{ft} \times 8\ \text{ft} \times 9\ \text{ft} \]
\[ V_{\text{rectangular}} = 576\ \text{cubic feet} \]
2. **Volume of the square pyramid:**
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{height} \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times (8\ \text{ft} \times 8\ \text{ft}) \times 3\ \text{ft} \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 64\ \text{square feet} \times 3\ \text{ft} \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 192\ \text{cubic feet} \]
\[ V_{\text{pyramid}} = 64\ \text{cubic feet} \]
3. **Total volume of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa88d205-dd76-4939-b9bf-fa2466cfe1d2%2F1a3b0407-05e0-48da-baa7-d22bf58be18a%2Fuht5zc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem: Calculating the Volume of a Vendor's Tent
**Problem Statement:**
A vendor is using an 8 ft by 8 ft tent for a craft fair. The legs of the tent are 9 ft tall, and the top forms a square pyramid with a height of 3 ft.
**Question:**
What is the volume, in cubic feet, of space the tent occupies?
**Diagram Explanation:**
The diagram illustrates a tent composed of two parts:
1. **A rectangular base (prism)** - The base dimensions are 8 feet by 8 feet, and it has a height of 9 feet.
2. **A square pyramid on top** - The base of this pyramid coincides with the top of the rectangular prism, and it has a height of 3 feet.
**Dimensions:**
- Base of the tent: 8 ft x 8 ft
- Height of the rectangular part: 9 ft
- Height of the pyramid: 3 ft
**Steps to Calculate the Volume:**
1. **Volume of the rectangular base:**
\[ V_{\text{rectangular}} = \text{length} \times \text{width} \times \text{height} \]
\[ V_{\text{rectangular}} = 8\ \text{ft} \times 8\ \text{ft} \times 9\ \text{ft} \]
\[ V_{\text{rectangular}} = 576\ \text{cubic feet} \]
2. **Volume of the square pyramid:**
\[ V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{height} \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times (8\ \text{ft} \times 8\ \text{ft}) \times 3\ \text{ft} \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 64\ \text{square feet} \times 3\ \text{ft} \]
\[ V_{\text{pyramid}} = \frac{1}{3} \times 192\ \text{cubic feet} \]
\[ V_{\text{pyramid}} = 64\ \text{cubic feet} \]
3. **Total volume of
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