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
Find the volume of the triangular prism
![### 11.5 Volumes of Prisms & Cylinders
**Find the volume of the triangular prism.**
**Do not type units**
[Image of a triangular prism]
- The base of the triangle has a width of 9 yards.
- The height of the triangle (distance from the base to the top) is 15 yards.
- The length of the prism (distance along the side) is 12 yards.
**(Answer Box: 1620 yd³)**
In the context of solving this problem, here’s a step-by-step explanation:
1. **Find the Area of the Triangular Base:**
- The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
- Here, the base is 9 yards and the height is 15 yards.
- Substituting the values, we get:
\[
\text{Area} = \frac{1}{2} \times 9 \, \text{yd} \times 15 \, \text{yd} = \frac{1}{2} \times 135 \, \text{yd}^2 = 67.5 \, \text{yd}^2
\]
2. **Calculate the Volume of the Prism:**
- The volume formula for a prism is \( \text{Volume} = \text{Base Area} \times \text{length} \).
- Using the base area calculated above and the given length of 12 yards:
\[
\text{Volume} = 67.5 \, \text{yd}^2 \times 12 \, \text{yd} = 810 \, \text{yd}^3
\]
3. **Result:**
- The volume of the triangular prism is 810 cubic yards, but the prefilled answer box incorrectly displays "1620 yd³". The correct volume is 810 yd³.
**Diagram Explanation:**
The diagram illustrates a triangular prism with its dimensions labeled. The base of the triangle is aligned horizontally, showing a length of 9 yards. From the base, a vertical height measuring 15 yards reaches the top vertex of the triangle. The prism extends horizontally with a side length of 12 yards, representing the depth of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e9d242-cb37-4bc8-a74f-f7cca1efbc15%2F24169ce8-a5af-44e3-a4cd-fcf418fb1e02%2Fu8h2zik_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 11.5 Volumes of Prisms & Cylinders
**Find the volume of the triangular prism.**
**Do not type units**
[Image of a triangular prism]
- The base of the triangle has a width of 9 yards.
- The height of the triangle (distance from the base to the top) is 15 yards.
- The length of the prism (distance along the side) is 12 yards.
**(Answer Box: 1620 yd³)**
In the context of solving this problem, here’s a step-by-step explanation:
1. **Find the Area of the Triangular Base:**
- The formula for the area of a triangle is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
- Here, the base is 9 yards and the height is 15 yards.
- Substituting the values, we get:
\[
\text{Area} = \frac{1}{2} \times 9 \, \text{yd} \times 15 \, \text{yd} = \frac{1}{2} \times 135 \, \text{yd}^2 = 67.5 \, \text{yd}^2
\]
2. **Calculate the Volume of the Prism:**
- The volume formula for a prism is \( \text{Volume} = \text{Base Area} \times \text{length} \).
- Using the base area calculated above and the given length of 12 yards:
\[
\text{Volume} = 67.5 \, \text{yd}^2 \times 12 \, \text{yd} = 810 \, \text{yd}^3
\]
3. **Result:**
- The volume of the triangular prism is 810 cubic yards, but the prefilled answer box incorrectly displays "1620 yd³". The correct volume is 810 yd³.
**Diagram Explanation:**
The diagram illustrates a triangular prism with its dimensions labeled. The base of the triangle is aligned horizontally, showing a length of 9 yards. From the base, a vertical height measuring 15 yards reaches the top vertex of the triangle. The prism extends horizontally with a side length of 12 yards, representing the depth of the
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning