Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 14A
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Question
![**Finding the Volume of a Rectangular Pyramid**
To calculate the volume of a rectangular pyramid, use the following formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In the provided diagram, the dimensions of the pyramid are as follows:
- Length of the base (l) = 7 m
- Width of the base (w) = 3 m
- Height of the pyramid (h) = 6 m
**Step-by-Step Solution:**
1. **Calculate the Area of the Base:**
\[ \text{Base Area} = l \times w \]
\[ \text{Base Area} = 7 \, \text{m} \times 3 \, \text{m} \]
\[ \text{Base Area} = 21 \, \text{m}^2 \]
2. **Use the Formula for Volume:**
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
\[ V = \frac{1}{3} \times 21 \, \text{m}^2 \times 6 \, \text{m} \]
\[ V = \frac{1}{3} \times 126 \, \text{m}^3 \]
\[ V = 42 \, \text{m}^3 \]
**Final Volume:**
The volume of the rectangular pyramid is \( 42 \, \text{m}^3 \).
**Explanation of the Diagram:**
- The diagram shows a rectangular pyramid with its base having dimensions 7 meters (length) and 3 meters (width).
- The vertical height from the center of the base to the apex of the pyramid is 6 meters.
- There are selection options for units, where the correct choice for volume is \( \text{m}^3 \).
Remember to always include the correct unit (in this case, cubic meters) when reporting your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb12218e8-a364-4d7b-9622-abb2418bb64e%2F3ce93441-b5ea-4502-ae93-dd012a96df65%2Fkrwes0l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Volume of a Rectangular Pyramid**
To calculate the volume of a rectangular pyramid, use the following formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In the provided diagram, the dimensions of the pyramid are as follows:
- Length of the base (l) = 7 m
- Width of the base (w) = 3 m
- Height of the pyramid (h) = 6 m
**Step-by-Step Solution:**
1. **Calculate the Area of the Base:**
\[ \text{Base Area} = l \times w \]
\[ \text{Base Area} = 7 \, \text{m} \times 3 \, \text{m} \]
\[ \text{Base Area} = 21 \, \text{m}^2 \]
2. **Use the Formula for Volume:**
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
\[ V = \frac{1}{3} \times 21 \, \text{m}^2 \times 6 \, \text{m} \]
\[ V = \frac{1}{3} \times 126 \, \text{m}^3 \]
\[ V = 42 \, \text{m}^3 \]
**Final Volume:**
The volume of the rectangular pyramid is \( 42 \, \text{m}^3 \).
**Explanation of the Diagram:**
- The diagram shows a rectangular pyramid with its base having dimensions 7 meters (length) and 3 meters (width).
- The vertical height from the center of the base to the apex of the pyramid is 6 meters.
- There are selection options for units, where the correct choice for volume is \( \text{m}^3 \).
Remember to always include the correct unit (in this case, cubic meters) when reporting your answer.
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