Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
Related questions
Question
![### Finding the Volume of a Pyramid
To determine the volume of a pyramid, we can use the following geometric formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
#### Given Measurements:
- The base of the pyramid is a rectangle with a width of 10 meters and a length of 18 meters.
- The height (perpendicular distance from the apex to the center of the base) is 5 meters.
### Step-by-Step Calculation:
1. **Calculate the Base Area (A):**
\[ A = \text{length} \times \text{width} \]
\[ A = 18 \, \text{m} \times 10 \, \text{m} \]
\[ A = 180 \, \text{square meters (m}^2\text{)} \]
2. **Calculate the Volume (V):**
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
\[ V = \frac{1}{3} \times 180 \, \text{m}^2 \times 5 \, \text{m} \]
\[ V = \frac{1}{3} \times 900 \, \text{cubic meters (m}^3\text{)} \]
\[ V = 300 \, \text{cubic meters (m}^3\text{)} \]
### Graphical Representation:
The image displays a 3-dimensional pyramid drawn with dashed lines indicating dimensions:
- The base of the pyramid is rectangular with lengths of 10 meters (width) and 18 meters (length).
- The height from the center of the base to the apex is marked as 5 meters.
### Final Volume:
Thus, the volume of the pyramid is:
\[ \text{The volume is } 300 \text{ cubic meters.} \]
Understanding these steps allows for solving similar problems by applying appropriate geometric formulas and calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e7bbe56-6e0f-4e60-be65-bd82ac2b3970%2Fe45a6e95-c201-4afc-8c5b-64222fffefa3%2F9r71iea_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Volume of a Pyramid
To determine the volume of a pyramid, we can use the following geometric formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
#### Given Measurements:
- The base of the pyramid is a rectangle with a width of 10 meters and a length of 18 meters.
- The height (perpendicular distance from the apex to the center of the base) is 5 meters.
### Step-by-Step Calculation:
1. **Calculate the Base Area (A):**
\[ A = \text{length} \times \text{width} \]
\[ A = 18 \, \text{m} \times 10 \, \text{m} \]
\[ A = 180 \, \text{square meters (m}^2\text{)} \]
2. **Calculate the Volume (V):**
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
\[ V = \frac{1}{3} \times 180 \, \text{m}^2 \times 5 \, \text{m} \]
\[ V = \frac{1}{3} \times 900 \, \text{cubic meters (m}^3\text{)} \]
\[ V = 300 \, \text{cubic meters (m}^3\text{)} \]
### Graphical Representation:
The image displays a 3-dimensional pyramid drawn with dashed lines indicating dimensions:
- The base of the pyramid is rectangular with lengths of 10 meters (width) and 18 meters (length).
- The height from the center of the base to the apex is marked as 5 meters.
### Final Volume:
Thus, the volume of the pyramid is:
\[ \text{The volume is } 300 \text{ cubic meters.} \]
Understanding these steps allows for solving similar problems by applying appropriate geometric formulas and calculations.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
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
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
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
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL