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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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
![### Volume Calculation of a Triangular Prism
**Question:**
What is the volume?
**Description of the Diagram:**
- The diagram depicts an oblique triangular prism.
- The base of the triangular face is \(12 \text{ m}\).
- The height of the triangular face is \(12 \text{ m}\) (vertical dashed line).
- The length of the prism (distance between the triangular faces) is \(5 \text{ m}\).
**Volume Formula for a Triangular Prism:**
To calculate the volume of a triangular prism, you can use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Length} \]
**Base Area Calculation:**
The area of the triangular base can be found using the formula for the area of a triangle:
\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Given:
- Base (b) = \(12 \text{ m}\)
- Height (h) = \(12 \text{ m}\)
Thus,
\[ \text{Base Area} = \frac{1}{2} \times 12 \text{ m} \times 12 \text{ m} = 72 \text{ m}^2 \]
**Volume Calculation:**
Using the calculated base area and the given length of the prism:
\[ \text{Volume} = 72 \text{ m}^2 \times 5 \text{ m} = 360 \text{ m}^3 \]
**Answer:**
The volume of the triangular prism is \(\boxed{360}\) cubic meters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf941769-c17e-48ea-9867-86fabfbc8a11%2Fdb5e31e7-22bd-4f0f-8073-0768270da8e1%2Fget3ab9_processed.png&w=3840&q=75)
Transcribed Image Text:### Volume Calculation of a Triangular Prism
**Question:**
What is the volume?
**Description of the Diagram:**
- The diagram depicts an oblique triangular prism.
- The base of the triangular face is \(12 \text{ m}\).
- The height of the triangular face is \(12 \text{ m}\) (vertical dashed line).
- The length of the prism (distance between the triangular faces) is \(5 \text{ m}\).
**Volume Formula for a Triangular Prism:**
To calculate the volume of a triangular prism, you can use the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Length} \]
**Base Area Calculation:**
The area of the triangular base can be found using the formula for the area of a triangle:
\[ \text{Base Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Given:
- Base (b) = \(12 \text{ m}\)
- Height (h) = \(12 \text{ m}\)
Thus,
\[ \text{Base Area} = \frac{1}{2} \times 12 \text{ m} \times 12 \text{ m} = 72 \text{ m}^2 \]
**Volume Calculation:**
Using the calculated base area and the given length of the prism:
\[ \text{Volume} = 72 \text{ m}^2 \times 5 \text{ m} = 360 \text{ m}^3 \]
**Answer:**
The volume of the triangular prism is \(\boxed{360}\) cubic meters.
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