# Work problem, deals with great pyramid

• stangeroo
In summary, the conversation discusses a calculus problem involving finding the volume and work against gravity of the Great Pyramid of Cheops, with a density of 200lb/ft^3. The first part involves integrating the volume of each slab with a thickness of deltaX or deltaY, while the second part involves calculating the work done on each differential mass element using the formula mgh. The area, volume, and weight of each horizontal slice can be expressed as functions of y, and the work done is equal to the weight times the height.
stangeroo
this is a calc problem, but I thought it fits better here than in the math section since its homework.

Here it goes:

the great pyramid of cheops is 410 feet tall and 755 feet square at the base. find the volume of the pyramid using calculus.

Part two:
The stone used in constructing it has a density of 200lb/ft^3. Find the work against gravity in building the pyramid.

I understand you integrate from 0 to 410 of the volume of each slab with a thickness of deltaX(or would it be delta y?) I am unsure how to calculate part two though, i haven't had much experience with work and force. anyone want to drop a hint or two

You're right on the first part, and it doesn't matter what you call the integration variable. For the second part, the work done raising a mass m by a height h against a gravitational acceleration g is mgh. Add up the work done on each differential mass element ρdV, where ρ is the density.

For each horizontal slice, its area, its volume, and its weight can all be expressed as functions of y (distance from the x-axis). And for each slice, the work done is equal to the weight times the height.

## 1. How were the massive stones used to build the Great Pyramid transported and placed?

The most widely accepted theory is that the stones were transported on wooden sledges and placed using ramps made of mud bricks. However, there is ongoing debate and research about other possible methods.

## 2. How long did it take to build the Great Pyramid?

The Great Pyramid is estimated to have taken approximately 20 years to build, with construction starting around 2560 BC and finishing around 2540 BC. This was a massive undertaking that required thousands of workers.

## 3. What tools and techniques were used to construct the Great Pyramid?

The ancient Egyptians used a variety of tools and techniques to construct the Great Pyramid, including wooden sledges, ropes, levers, and pulleys. They also used a surveying tool called a plumb bob to ensure the accuracy of the pyramid's alignment.

## 4. How did the ancient Egyptians align the Great Pyramid with the cardinal directions?

The ancient Egyptians were skilled astronomers and used the stars to align the Great Pyramid with the cardinal directions. They likely used a tool called a merkhet, which allowed them to track the movement of specific stars and determine the north-south and east-west directions.

## 5. What was the purpose of the Great Pyramid?

The exact purpose of the Great Pyramid is still debated, but it is believed to have served as a tomb for the pharaoh Khufu. It may also have had religious and political significance, as well as serving as a symbol of the pharaoh's power and authority.

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