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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Calculate volume
To calculate the volume of this right triangular prism, use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Prism Height} \]
First, find the area of the triangular base:
\[ \text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Base Area} = \frac{1}{2} \times 12 \, \text{m} \times 9 \, \text{m} \]
\[ \text{Base Area} = 54 \, \text{m}^2 \]
Now, multiply this area by the depth/length of the prism to find the volume:
\[ \text{Volume} = 54 \, \text{m}^2 \times 24 \, \text{m} \]
\[ \text{Volume} = 1296 \, \text{m}^3 \]
Therefore, the volume of the right triangular prism is:
\[ \boxed{1296 \, \text{m}^3} \]
**Multiple Choice Options:**
A. 1080 m³
B. 648 m³
C. 1296 m³
D. 918 m³
Select the correct answer from the options above.
Explanation:
- Based on the calculations, the correct answer is option **C. 1296 m³**.
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### Calculate the Volume of a Right Triangular Prism
Given the right triangular prism with the following dimensions:
- Height of the triangle: 9 meters
- Base of the triangle: 12 meters
- Depth/length of the prism: 24 meters
Diagram of the prism is shown below:
To calculate the volume of this right triangular prism, use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Prism Height} \]
First, find the area of the triangular base:
\[ \text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Base Area} = \frac{1}{2} \times 12 \, \text{m} \times 9 \, \text{m} \]
\[ \text{Base Area} = 54 \, \text{m}^2 \]
Now, multiply this area by the depth/length of the prism to find the volume:
\[ \text{Volume} = 54 \, \text{m}^2 \times 24 \, \text{m} \]
\[ \text{Volume} = 1296 \, \text{m}^3 \]
Therefore, the volume of the right triangular prism is:
\[ \boxed{1296 \, \text{m}^3} \]
**Multiple Choice Options:**
A. 1080 m³
B. 648 m³
C. 1296 m³
D. 918 m³
Select the correct answer from the options above.
Explanation:
- Based on the calculations, the correct answer is option **C. 1296 m³**.
---
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