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
Concept explainers
Power Operation
Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.
Exponents
The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.
Question
Transcribed Image Text:**Question:**
Find the volume of this rectangular pyramid.
Be sure to include the correct unit in your answer.
![### Geometry of a Square-Based Pyramid
**Diagram Description:**
This diagram represents a square-based pyramid with key measurements labeled.
- **Base Dimensions:**
- The length of each side of the square base is 9 cm.
- One side on the base plane is marked with a dimension of 5 cm, indicating a possible segment or distance of interest on that side.
- **Height of Pyramid:**
- The vertical height from the base to the apex (top point) of the pyramid is also 9 cm.
- **Other Notable Features:**
- There is a dashed blue line representing the height and indicating it stands perpendicular to the base.
- The right-angle symbol at the intersection of the height line and the base confirms this perpendicularity.
This diagram can be used to understand the dimensional properties of a square-based pyramid, including calculations related to volume, slant height, or surface area.
#### Key Points for Further Study:
1. **Volume of a Square-Based Pyramid:**
The volume \( V \) can be found using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times (9 \, \text{cm} \times 9 \, \text{cm}) \times 9 \, \text{cm}
\]
2. **Surface Area:**
The surface area includes the base area and the four triangular faces. Each triangular face's area can be calculated using the slant height, which can be derived using the Pythagorean theorem if needed.
3. **Slant Height:**
The slant height can be calculated using the Pythagorean theorem in the right-angled triangle formed by the slant height, half of the base side length (4.5 cm), and the vertical height (9 cm).
This geometric shape is a classic problem area within solid geometry, providing essential practical applications and problem-solving experiences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6373081f-17d9-417b-b535-bd8706276caa%2F9e09c41c-109d-4a78-baf7-a06c270aaf13%2Fdeh321g_processed.png&w=3840&q=75)
Transcribed Image Text:### Geometry of a Square-Based Pyramid
**Diagram Description:**
This diagram represents a square-based pyramid with key measurements labeled.
- **Base Dimensions:**
- The length of each side of the square base is 9 cm.
- One side on the base plane is marked with a dimension of 5 cm, indicating a possible segment or distance of interest on that side.
- **Height of Pyramid:**
- The vertical height from the base to the apex (top point) of the pyramid is also 9 cm.
- **Other Notable Features:**
- There is a dashed blue line representing the height and indicating it stands perpendicular to the base.
- The right-angle symbol at the intersection of the height line and the base confirms this perpendicularity.
This diagram can be used to understand the dimensional properties of a square-based pyramid, including calculations related to volume, slant height, or surface area.
#### Key Points for Further Study:
1. **Volume of a Square-Based Pyramid:**
The volume \( V \) can be found using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times (9 \, \text{cm} \times 9 \, \text{cm}) \times 9 \, \text{cm}
\]
2. **Surface Area:**
The surface area includes the base area and the four triangular faces. Each triangular face's area can be calculated using the slant height, which can be derived using the Pythagorean theorem if needed.
3. **Slant Height:**
The slant height can be calculated using the Pythagorean theorem in the right-angled triangle formed by the slant height, half of the base side length (4.5 cm), and the vertical height (9 cm).
This geometric shape is a classic problem area within solid geometry, providing essential practical applications and problem-solving experiences.
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
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