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
Question
![### Pyramid Volume Calculation
**Problem Statement:**
8. Find the VOLUME of the pyramid that I'm looking at. It is 147 m on each side and 139 m high *
Below the problem statement, there is an image of a pyramid taken from an elevated point of view. The photographer’s feet can be seen at the bottom of the image, looking down toward the majestic pyramid structure. The surrounding area appears to be desert land with some structures visible in the vicinity.
**Solution:**
To calculate the volume of the pyramid, we will use the formula for the volume of a square pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given:
- Base side length \( a = 147 \) meters
- Height \( h = 139 \) meters
First, we calculate the area of the base:
\[ \text{Base Area} = a^2 = 147^2 = 21,609 \text{ square meters} \]
Then, substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 21,609 \times 139 \]
\[ V = \frac{1}{3} \times 3,004,851 \]
\[ V = 1,001,617 \text{ cubic meters} \]
**Conclusion:**
The volume of the pyramid is **1,001,617 cubic meters**.
This problem illustrates the application of geometric formulas to find the volume of a real-world structure, enhancing understanding of mathematical concepts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5879a50f-f71e-408e-bdd0-9b0f63c8eb2e%2Fbeaca123-3f2c-417a-b050-9b134ce2c4d1%2F3rqvbbi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Pyramid Volume Calculation
**Problem Statement:**
8. Find the VOLUME of the pyramid that I'm looking at. It is 147 m on each side and 139 m high *
Below the problem statement, there is an image of a pyramid taken from an elevated point of view. The photographer’s feet can be seen at the bottom of the image, looking down toward the majestic pyramid structure. The surrounding area appears to be desert land with some structures visible in the vicinity.
**Solution:**
To calculate the volume of the pyramid, we will use the formula for the volume of a square pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given:
- Base side length \( a = 147 \) meters
- Height \( h = 139 \) meters
First, we calculate the area of the base:
\[ \text{Base Area} = a^2 = 147^2 = 21,609 \text{ square meters} \]
Then, substitute the base area and height into the volume formula:
\[ V = \frac{1}{3} \times 21,609 \times 139 \]
\[ V = \frac{1}{3} \times 3,004,851 \]
\[ V = 1,001,617 \text{ cubic meters} \]
**Conclusion:**
The volume of the pyramid is **1,001,617 cubic meters**.
This problem illustrates the application of geometric formulas to find the volume of a real-world structure, enhancing understanding of mathematical concepts.
![**Lesson: Calculating the Volume of a Rectangular Fish Tank**
**Example Question:**
*Find the VOLUME of my fish tank.*
**Description:**
In the given image, you see a rectangular fish tank with the following dimensions:
- Length: 48 inches
- Width: 13 inches
- Height: 21 inches
These measurements are marked clearly on the image with dotted lines illustrating each dimension.
To find the volume of the fish tank, we can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
**Calculation Steps:**
1. Identify the dimensions:
- Length (L) = 48 inches
- Width (W) = 13 inches
- Height (H) = 21 inches
2. Plug the values into the formula:
\[ \text{Volume} = 48 \text{ in} \times 13 \text{ in} \times 21 \text{ in} \]
3. Multiply the values:
\[ \text{Volume} = 48 \times 13 \times 21 \]
Let's calculate step by step:
\[ 48 \times 13 = 624 \]
\[ 624 \times 21 = 13,104 \]
So the volume of the fish tank is \( 13,104 \) cubic inches.
**Summary:**
The fish tank in the image has a volume of **13,104 cubic inches**. This calculation helps you understand how to determine the space inside a rectangular container, which is essential for knowing how much water is required to fill it.
**Note:** Volumes in aquariums are frequently also expressed in gallons. There are 231 cubic inches in a gallon. To convert cubic inches to gallons:
\[ \text{Volume in gallons} = \frac{\text{Volume in cubic inches}}{231} \]
So, for the given volume:
\[ \text{Volume in gallons} = \frac{13,104}{231} \approx 56.7 \text{ gallons} \]
The fish tank can hold approximately **56.7 gallons** of water.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5879a50f-f71e-408e-bdd0-9b0f63c8eb2e%2Fbeaca123-3f2c-417a-b050-9b134ce2c4d1%2Fop9nu8r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Lesson: Calculating the Volume of a Rectangular Fish Tank**
**Example Question:**
*Find the VOLUME of my fish tank.*
**Description:**
In the given image, you see a rectangular fish tank with the following dimensions:
- Length: 48 inches
- Width: 13 inches
- Height: 21 inches
These measurements are marked clearly on the image with dotted lines illustrating each dimension.
To find the volume of the fish tank, we can use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
**Calculation Steps:**
1. Identify the dimensions:
- Length (L) = 48 inches
- Width (W) = 13 inches
- Height (H) = 21 inches
2. Plug the values into the formula:
\[ \text{Volume} = 48 \text{ in} \times 13 \text{ in} \times 21 \text{ in} \]
3. Multiply the values:
\[ \text{Volume} = 48 \times 13 \times 21 \]
Let's calculate step by step:
\[ 48 \times 13 = 624 \]
\[ 624 \times 21 = 13,104 \]
So the volume of the fish tank is \( 13,104 \) cubic inches.
**Summary:**
The fish tank in the image has a volume of **13,104 cubic inches**. This calculation helps you understand how to determine the space inside a rectangular container, which is essential for knowing how much water is required to fill it.
**Note:** Volumes in aquariums are frequently also expressed in gallons. There are 231 cubic inches in a gallon. To convert cubic inches to gallons:
\[ \text{Volume in gallons} = \frac{\text{Volume in cubic inches}}{231} \]
So, for the given volume:
\[ \text{Volume in gallons} = \frac{13,104}{231} \approx 56.7 \text{ gallons} \]
The fish tank can hold approximately **56.7 gallons** of water.
Expert Solution
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 3 steps with 3 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