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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Question
Please assist explain this volume.
![**Calculate the volume of the square pyramid.**
The image shows a square pyramid with a base length of 10 feet and a height of 13 feet.
To calculate the volume of a square pyramid, use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
1. **Base Area**: Since the base is a square, calculate the area as follows:
\[ \text{Base Area} = \text{side}^2 = 10 \, \text{ft} \times 10 \, \text{ft} = 100 \, \text{ft}^2 \]
2. **Volume Calculation**:
\[ V = \frac{1}{3} \times 100 \, \text{ft}^2 \times 13 \, \text{ft} = \frac{1300}{3} \, \text{ft}^3 \approx 433.33 \, \text{ft}^3 \]
The volume of the square pyramid is approximately 433.33 cubic feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ca575c3-e7a0-4200-8af2-09dad4314965%2F7b58a139-d3cf-4869-9846-cb9d3c724743%2F300jzm.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculate the volume of the square pyramid.**
The image shows a square pyramid with a base length of 10 feet and a height of 13 feet.
To calculate the volume of a square pyramid, use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
1. **Base Area**: Since the base is a square, calculate the area as follows:
\[ \text{Base Area} = \text{side}^2 = 10 \, \text{ft} \times 10 \, \text{ft} = 100 \, \text{ft}^2 \]
2. **Volume Calculation**:
\[ V = \frac{1}{3} \times 100 \, \text{ft}^2 \times 13 \, \text{ft} = \frac{1300}{3} \, \text{ft}^3 \approx 433.33 \, \text{ft}^3 \]
The volume of the square pyramid is approximately 433.33 cubic feet.
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