3. A solid pyramid is 140 m in height, and has a square base with side length 200 m. It is made of stone with a density of 1600 kg/m³. How much work did it take to build the pyramid? (This is like a water pumping problem, but instead of "lifting" the water to a particular height, the material to build each part of the pyramid is lifted from the ground.)
3. A solid pyramid is 140 m in height, and has a square base with side length 200 m. It is made of stone with a density of 1600 kg/m³. How much work did it take to build the pyramid? (This is like a water pumping problem, but instead of "lifting" the water to a particular height, the material to build each part of the pyramid is lifted from the ground.)
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Transcribed Image Text:**Problem Statement on Educational Website:**
3. A solid pyramid is 140 m in height and has a square base with side length 200 m. It is made of stone with a density of 1600 kg/m³. How much work did it take to build the pyramid? (This is like a water pumping problem, but instead of "lifting" the water to a particular height, the material to build each part of the pyramid is lifted from the ground.)
**Contextual Diagram:**
Imagine a pyramid that rises to a height of 140 meters, with a base that is a square with each side measuring 200 meters. The pyramid is constructed using stone, and the density of this stone is 1600 kilograms per cubic meter. The task is to calculate the amount of work required to assemble such a structure by lifting the stone from the ground level up to the necessary points in the pyramid during construction.
**Explanation of the Physical Concept:**
The work needed for construction can be determined by integrating the gravitational force over the height of the pyramid. This concept is analogous to calculating the work required to pump water to a certain height, replacing water with stone materials in this scenario.
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