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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![**Finding the Volume of a Rectangular Pyramid**
To determine the volume of a rectangular pyramid, a student should follow the established formula for volume calculation and carefully apply the given dimensions.
**Problem Statement:**
Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer.
**Given Dimensions and Diagram Explanation:**
- The base of the pyramid is a rectangle with one side measuring 9 yards (yd) and the other side measuring 5 yards (yd).
- The height (h) of the pyramid from the base to the apex (top point) is 6 yards (yd).
**Steps to Solve:**
1. **Identify the formula for the volume of a pyramid:**
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
2. **Calculate the area of the base:**
The base is a rectangle, so the area (A) is given by:
\[
\text{Base Area} = \text{length} \times \text{width} = 9 \, \text{yd} \times 5 \, \text{yd} = 45 \, \text{yd}^2
\]
3. **Plug the base area and height into the volume formula:**
Given that the height (h) of the pyramid is 6 yd,
\[
\text{Volume} = \frac{1}{3} \times 45 \, \text{yd}^2 \times 6 \, \text{yd}
\]
4. **Perform the multiplication:**
\[
V = \frac{1}{3} \times 270 \, \text{yd}^3 = 90 \, \text{yd}^3
\]
Therefore, the volume of the rectangular pyramid is \( 90 \, \text{yd}^3 \).
**Important Note:**
When inputting your answer, ensure to include the correct unit, which is cubic yards (\( \text{yd}^3 \)) in this case.
**Interactive Component:**
To input the answer into an educational platform, select the appropriate unit from the options: \( \text{yd}, \text{yd}^2, \text{yd}^3 \), and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f0cb9e0-878b-46ea-a9a5-5d8e401495e2%2F38acfc30-ce8b-4c4b-bd22-d99fc6423b2d%2Fjlelnc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Volume of a Rectangular Pyramid**
To determine the volume of a rectangular pyramid, a student should follow the established formula for volume calculation and carefully apply the given dimensions.
**Problem Statement:**
Find the volume of this rectangular pyramid. Be sure to include the correct unit in your answer.
**Given Dimensions and Diagram Explanation:**
- The base of the pyramid is a rectangle with one side measuring 9 yards (yd) and the other side measuring 5 yards (yd).
- The height (h) of the pyramid from the base to the apex (top point) is 6 yards (yd).
**Steps to Solve:**
1. **Identify the formula for the volume of a pyramid:**
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
2. **Calculate the area of the base:**
The base is a rectangle, so the area (A) is given by:
\[
\text{Base Area} = \text{length} \times \text{width} = 9 \, \text{yd} \times 5 \, \text{yd} = 45 \, \text{yd}^2
\]
3. **Plug the base area and height into the volume formula:**
Given that the height (h) of the pyramid is 6 yd,
\[
\text{Volume} = \frac{1}{3} \times 45 \, \text{yd}^2 \times 6 \, \text{yd}
\]
4. **Perform the multiplication:**
\[
V = \frac{1}{3} \times 270 \, \text{yd}^3 = 90 \, \text{yd}^3
\]
Therefore, the volume of the rectangular pyramid is \( 90 \, \text{yd}^3 \).
**Important Note:**
When inputting your answer, ensure to include the correct unit, which is cubic yards (\( \text{yd}^3 \)) in this case.
**Interactive Component:**
To input the answer into an educational platform, select the appropriate unit from the options: \( \text{yd}, \text{yd}^2, \text{yd}^3 \), and
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