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 havent 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.