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
![### Calculating the Volume of a Pyramid
**Problem Statement:**
Find the volume of a pyramid with a square base, where the perimeter of the base is 15.8 ft and the height of the pyramid is 20.4 ft. Round your answer to the nearest tenth of a cubic foot.
**Details:**
1. **Perimeter of the base (P):** 15.8 ft
2. **Height of the pyramid (h):** 20.4 ft
**Steps to Solve:**
1. **Find the side length of the square base:**
- Since the base is a square, and the perimeter \( P \) is given, the side length \( s \) of the square can be calculated using the formula:
\[
P = 4s \implies s = \frac{P}{4}
\]
Substitute \( P \) with 15.8 ft:
\[
s = \frac{15.8}{4} = 3.95 \text{ ft}
\]
2. **Calculate the area of the square base \( A \):**
- The area \( A \) of a square is given by:
\[
A = s^2
\]
Substitute \( s \) with 3.95 ft:
\[
A = (3.95)^2 = 15.6025 \text{ ft}^2
\]
3. **Calculate the volume \( V \) of the pyramid:**
- The volume \( V \) of a pyramid is calculated using the formula:
\[
V = \frac{1}{3} A h
\]
Substitute \( A \) with 15.6025 ft\(^2\) and \( h \) with 20.4 ft:
\[
V = \frac{1}{3} \times 15.6025 \times 20.4 = 106.1517 \text{ ft}^3
\]
4. **Round the volume to the nearest tenth:**
\[
V \approx 106.2 \text{ ft}^3
\]
**Conclusion:**
The volume of the pyramid is approximately \( 106.2 \) cubic feet.
**Answer Submission:**
- In the answer box provided, enter:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e91a5a9-6404-44a2-9b53-644c82ff080b%2F3660b958-d4c5-4a4c-a053-6d1f400e7344%2Fdaaxpg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Volume of a Pyramid
**Problem Statement:**
Find the volume of a pyramid with a square base, where the perimeter of the base is 15.8 ft and the height of the pyramid is 20.4 ft. Round your answer to the nearest tenth of a cubic foot.
**Details:**
1. **Perimeter of the base (P):** 15.8 ft
2. **Height of the pyramid (h):** 20.4 ft
**Steps to Solve:**
1. **Find the side length of the square base:**
- Since the base is a square, and the perimeter \( P \) is given, the side length \( s \) of the square can be calculated using the formula:
\[
P = 4s \implies s = \frac{P}{4}
\]
Substitute \( P \) with 15.8 ft:
\[
s = \frac{15.8}{4} = 3.95 \text{ ft}
\]
2. **Calculate the area of the square base \( A \):**
- The area \( A \) of a square is given by:
\[
A = s^2
\]
Substitute \( s \) with 3.95 ft:
\[
A = (3.95)^2 = 15.6025 \text{ ft}^2
\]
3. **Calculate the volume \( V \) of the pyramid:**
- The volume \( V \) of a pyramid is calculated using the formula:
\[
V = \frac{1}{3} A h
\]
Substitute \( A \) with 15.6025 ft\(^2\) and \( h \) with 20.4 ft:
\[
V = \frac{1}{3} \times 15.6025 \times 20.4 = 106.1517 \text{ ft}^3
\]
4. **Round the volume to the nearest tenth:**
\[
V \approx 106.2 \text{ ft}^3
\]
**Conclusion:**
The volume of the pyramid is approximately \( 106.2 \) cubic feet.
**Answer Submission:**
- In the answer box provided, enter:
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