Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.
Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.
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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![## Volume of a Pyramid Calculation
**Problem Statement:**
Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.
**Solution Steps:**
1. **Formula for the Volume of a Pyramid:**
The volume \( V \) of a pyramid is given by the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
2. **Calculate the Base Area:**
The base of the pyramid is a square. The area \( A \) of a square is calculated using the formula:
\[
A = \text{side length}^2
\]
Given that the side length of the base is 13.9 cm:
\[
A = 13.9 \, \text{cm} \times 13.9 \, \text{cm} = 193.21 \, \text{cm}^2
\]
3. **Calculate the Volume:**
Substitute the base area and the height into the volume formula:
\[
V = \frac{1}{3} \times 193.21 \, \text{cm}^2 \times 6.3 \, \text{cm}
\]
\[
V = \frac{1}{3} \times 1217.223 \, \text{cm}^3
\]
\[
V \approx 405.7 \, \text{cm}^3
\]
4. **Round the Answer:**
We round 405.7 to the nearest tenth of a cubic centimeter.
**Answer:**
\[
\boxed{405.7 \, \text{cm}^3}
\]
This completes the calculation for the volume of the pyramid based on the given dimensions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54ff0d6d-50ab-496d-8afd-66229ec49688%2F771ad4e8-0392-4105-a88d-19e0a23fc9c0%2Fz1tsgn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Volume of a Pyramid Calculation
**Problem Statement:**
Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.
**Solution Steps:**
1. **Formula for the Volume of a Pyramid:**
The volume \( V \) of a pyramid is given by the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
2. **Calculate the Base Area:**
The base of the pyramid is a square. The area \( A \) of a square is calculated using the formula:
\[
A = \text{side length}^2
\]
Given that the side length of the base is 13.9 cm:
\[
A = 13.9 \, \text{cm} \times 13.9 \, \text{cm} = 193.21 \, \text{cm}^2
\]
3. **Calculate the Volume:**
Substitute the base area and the height into the volume formula:
\[
V = \frac{1}{3} \times 193.21 \, \text{cm}^2 \times 6.3 \, \text{cm}
\]
\[
V = \frac{1}{3} \times 1217.223 \, \text{cm}^3
\]
\[
V \approx 405.7 \, \text{cm}^3
\]
4. **Round the Answer:**
We round 405.7 to the nearest tenth of a cubic centimeter.
**Answer:**
\[
\boxed{405.7 \, \text{cm}^3}
\]
This completes the calculation for the volume of the pyramid based on the given dimensions.
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