The Great Pyramid outside Cairo, Egypt, has a square base measuring 756 feet on a side and a height of 480 feet. a. What is the volume of the Great Pyramid, in cubic vards? b. The stones used to build the Great Pyramid were limestone blocks with an average volume of 1.5 cubic yards. Assuming a solid pyramid, how many of these blocks were needed to construct the Great Pyramid?
The Great Pyramid outside Cairo, Egypt, has a square base measuring 756 feet on a side and a height of 480 feet. a. What is the volume of the Great Pyramid, in cubic vards? b. The stones used to build the Great Pyramid were limestone blocks with an average volume of 1.5 cubic yards. Assuming a solid pyramid, how many of these blocks were needed to construct the Great Pyramid?
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
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![### The Great Pyramid of Giza - An Educational Exploration
#### The Great Pyramid outside Cairo, Egypt
The Great Pyramid, located near Cairo, Egypt, stands as a marvel of ancient architecture and engineering. Here, we break down some fundamental questions to delve into the pyramid's construction and how it was built.
#### Problem 1: Volume Calculation
**Given:**
- **Base Dimensions:** 756 feet on each side (square base)
- **Height:** 480 feet
##### Question:
**a. What is the volume of the Great Pyramid, in cubic yards?**
The volume \( V \) of a pyramid is calculated using the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, calculate the base area:
\[ \text{Base Area} = \text{side} \times \text{side} = 756 \times 756 \text{ square feet} \]
Next, calculate the volume in cubic feet:
\[ V = \frac{1}{3} \times 756^2 \times 480 \]
\[ V \approx 91,575,680 \text{ cubic feet} \]
Since 1 cubic yard equals 27 cubic feet, convert the volume to cubic yards:
\[ V_{yards} = \frac{91,575,680}{27} \]
\[ V_{yards} \approx 3,392,436 \text{ cubic yards} \]
Thus, the volume of the Great Pyramid is approximately 3,392,436 cubic yards.
#### Problem 2: Stone Calculation
##### Question:
**b. The stones used to build the Great Pyramid were limestone blocks with an average volume of 1.5 cubic yards. Assuming a solid pyramid, how many of these blocks were needed to construct the Great Pyramid?**
Given:
- **Average Volume of Each Block:** 1.5 cubic yards
Calculate the number of blocks:
\[ \text{Number of Blocks} = \frac{\text{Total Volume of Pyramid}}{\text{Volume of Each Block}} \]
\[ \text{Number of Blocks} = \frac{3,392,436}{1.5} \]
\[ \text{Number of Blocks} \approx 2,261,624 \]
Therefore, approximately 2,261,624 limestone blocks were needed to construct the Great](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae063e21-e069-49f8-ad73-1d555b7f1041%2F1f707dcf-9d2b-416a-846f-184c744df1c6%2F9hr5x7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### The Great Pyramid of Giza - An Educational Exploration
#### The Great Pyramid outside Cairo, Egypt
The Great Pyramid, located near Cairo, Egypt, stands as a marvel of ancient architecture and engineering. Here, we break down some fundamental questions to delve into the pyramid's construction and how it was built.
#### Problem 1: Volume Calculation
**Given:**
- **Base Dimensions:** 756 feet on each side (square base)
- **Height:** 480 feet
##### Question:
**a. What is the volume of the Great Pyramid, in cubic yards?**
The volume \( V \) of a pyramid is calculated using the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
First, calculate the base area:
\[ \text{Base Area} = \text{side} \times \text{side} = 756 \times 756 \text{ square feet} \]
Next, calculate the volume in cubic feet:
\[ V = \frac{1}{3} \times 756^2 \times 480 \]
\[ V \approx 91,575,680 \text{ cubic feet} \]
Since 1 cubic yard equals 27 cubic feet, convert the volume to cubic yards:
\[ V_{yards} = \frac{91,575,680}{27} \]
\[ V_{yards} \approx 3,392,436 \text{ cubic yards} \]
Thus, the volume of the Great Pyramid is approximately 3,392,436 cubic yards.
#### Problem 2: Stone Calculation
##### Question:
**b. The stones used to build the Great Pyramid were limestone blocks with an average volume of 1.5 cubic yards. Assuming a solid pyramid, how many of these blocks were needed to construct the Great Pyramid?**
Given:
- **Average Volume of Each Block:** 1.5 cubic yards
Calculate the number of blocks:
\[ \text{Number of Blocks} = \frac{\text{Total Volume of Pyramid}}{\text{Volume of Each Block}} \]
\[ \text{Number of Blocks} = \frac{3,392,436}{1.5} \]
\[ \text{Number of Blocks} \approx 2,261,624 \]
Therefore, approximately 2,261,624 limestone blocks were needed to construct the Great
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