The height of a square pyramid is one half the length of each side. The volume of the pyramid is 2,304 in.3. What is the height of the pyramid? height = in.
The height of a square pyramid is one half the length of each side. The volume of the pyramid is 2,304 in.3. What is the height of the pyramid? height = in.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.8: Volumes Of Pyramids And Cones
Problem 17E
Related questions
Question
![### Geometry Problem - Volume of a Square Pyramid
**Question:**
The height of a square pyramid is one half the length of each side. The volume of the pyramid is 2,304 in³. What is the height of the pyramid?
**Given:**
- Volume of square pyramid (V) = 2,304 in³
- Height (h) = ½ * side length (s)
**To Find:**
- Height (h) in inches.
**Formula:**
The volume (V) of a square pyramid is given by:
\[ V = \frac{1}{3} \times s^2 \times h \]
Where:
- \( s \) is the length of the side of the base
- \( h \) is the height of the pyramid
Since \( h = \frac{1}{2} \times s \), substitute \( \frac{1}{2} \times s \) in place of \( h \) in the volume formula:
\[ V = \frac{1}{3} \times s^2 \times \frac{1}{2} \times s \]
This simplifies to:
\[ V = \frac{1}{6} \times s^3 \]
We know \( V = 2,304 \):
\[ 2,304 = \frac{1}{6} \times s^3 \]
To find \( s \):
\[ s^3 = 2,304 \times 6 \]
\[ s^3 = 13,824 \]
\[ s = \sqrt[3]{13,824} \]
\[ s \approx 24 \]
Now we use the relationship \( h = \frac{1}{2} \times s \):
\[ h = \frac{1}{2} \times 24 \]
\[ h = 12 \]
**Answer:**
Height \( h = \boxed{12 \text{ inches}} \)
**Interactive Elements:**
- **Review progress** button to check the answers.
- **Question Navigation:** This is question 8 out of 12, with options to move **Back** or **Next**.
This example demonstrates the application of volume formulas for solid geometrical shapes and the integration of variable relationships.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d730b9d-41b9-44d3-ac16-130c51dd79cf%2Fc3ae0922-50c4-4ec1-be32-41c81e6c383c%2F5xm13af_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem - Volume of a Square Pyramid
**Question:**
The height of a square pyramid is one half the length of each side. The volume of the pyramid is 2,304 in³. What is the height of the pyramid?
**Given:**
- Volume of square pyramid (V) = 2,304 in³
- Height (h) = ½ * side length (s)
**To Find:**
- Height (h) in inches.
**Formula:**
The volume (V) of a square pyramid is given by:
\[ V = \frac{1}{3} \times s^2 \times h \]
Where:
- \( s \) is the length of the side of the base
- \( h \) is the height of the pyramid
Since \( h = \frac{1}{2} \times s \), substitute \( \frac{1}{2} \times s \) in place of \( h \) in the volume formula:
\[ V = \frac{1}{3} \times s^2 \times \frac{1}{2} \times s \]
This simplifies to:
\[ V = \frac{1}{6} \times s^3 \]
We know \( V = 2,304 \):
\[ 2,304 = \frac{1}{6} \times s^3 \]
To find \( s \):
\[ s^3 = 2,304 \times 6 \]
\[ s^3 = 13,824 \]
\[ s = \sqrt[3]{13,824} \]
\[ s \approx 24 \]
Now we use the relationship \( h = \frac{1}{2} \times s \):
\[ h = \frac{1}{2} \times 24 \]
\[ h = 12 \]
**Answer:**
Height \( h = \boxed{12 \text{ inches}} \)
**Interactive Elements:**
- **Review progress** button to check the answers.
- **Question Navigation:** This is question 8 out of 12, with options to move **Back** or **Next**.
This example demonstrates the application of volume formulas for solid geometrical shapes and the integration of variable relationships.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 4 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
![Trigonometry (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652224/9781305652224_smallCoverImage.gif)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
![PREALGEBRA](https://www.bartleby.com/isbn_cover_images/9781938168994/9781938168994_smallCoverImage.gif)