Question

I need help with this calculus question.
Some ancient Egyptians decided to build a pyramid with a square base that measured 750 feet on a side. The height of the pyramid was 500 feet. The density of the rock used in construction was 120 pounds per cubic foot.
It was assumed that the work force would remain constant. Each laborer could do 160 foot pounds of work per hour, working 12 hour days for 330 days per year for 20 years.
Determine, under these conditions, the number of laborers needed to construct the pyramid.

Answer 1

Is it a solid pyramid? you know, for ceremonial purposes :)

Answer 2

(1/3)*(750)^2*500 ft^3 * 120lbs/ft^3 * 1hr/(160lbs)/12hrs

Answer 3

yeah its solid

Answer 4

etc

Answer 5

i know its a definite integral equation that is the density * volume * distance(or ht.) I just can't figure out how to represent the volume.

Answer 6

888 laborers

Answer 7

(S) A(y) dy {0,h} or something like that.... but the formula for any conelike volume is (1/3)(Base Area)(height)...

Answer 8

intuition would say, find the amount of rock you need, figure out how much one laborer does in the alloted time span, then multiply that by how many laborers it take to do the job..... but other than that, I dont know...

Answer 9

\[\int\limits_{0}^{50}(120)(volume)(y)\]

the equation to find the work needed is something like this, i just can't figure out the section for volume.

Answer 10

50 should be 500

Answer 11

volume is integrated thru taking sections of the base area as it moves thru the height....

Answer 12

also the volume is representing the volume of a slice

Answer 13

each slice is x^2 dy in volume right?

Answer 14

and x changes with repect to height...or y

Answer 15

what is the slope of the face?

Answer 16

yeah basically, but the size of the slice changes since it is getting smaller going up

Answer 17

i don't know that isn't given

Answer 18

500/(750/2) would be a cross section of the "triangle"

Answer 19

the slope of a face is 500/375....might need to reduce.

the equation relating that to x and y is

y = -500/375(x) + 500

Answer 20

slope is 4/3 when reduced

Answer 21

x increase by 2 for every 3/4 increase in y .... if that helps

Answer 22

(3/2) (S) y dy {0,500} = (3/4) y^2 {0,500}

500^2 = 250000(3/4) = 750000/4 = 187500

that matches 500(750)/2 = 187500 for a flat area..... not sure how it helps tho :)

Answer 23

x^2 is the area of a normal base and it changes with respect to "y" at a rate of (3/2)(y) dy ?? It looks right, but this is still shakey ground fer me :)

Answer 24

yeah i think ive gotten it now, thanks.

Answer 25

if I messed up anything, youlet me know :)