What is the maximum height of the pyramid?

Question

For Awards Night at Baddeck High School, the math club is designing small solid silver pyramids. The base of the pyramids will be a 2-in-2-in square. The pyramids should not weigh more than 2 1/2 pounds. One cubic foot of silver weighs 655 pounds. What is the maximum height of the pyramid?

Answer 1

allrighty, so the first thin you gotta know is that

the volume of a pyramid is V = (1/3)*(Area of Base)*Height

you know that the area of the base is 4 (because 2*2 = 4)
now to solve for height you must find the "V"

but how do we do that you ask?
well by using the max poundage given to us

you know that 1ft3 of silver = 655 lbs
if you look up at google, 1ft3 = 1728in3 (or just do 12^3)

so now you have 1728in3 = 655 lbs
and you want to find what Volume (or in3) can i get with 2.5 lbs?

so you set up a proportion --> ("x"/1728) = (2.5/655)

solving for it, you get "x" to be roughly 6.6 (6.5954), and that is the maximum volume that you can have according to the weight limitations

now you plug everything back into ur regular eqn

and you have 6.6 = (1/3)*(4)*H
and you solve for H to get 4.95inches

Answer 2

If I remember, V(sq. pyramid)= b^2 (h/3), where b is the length of a square. This is a lot of dog-work with English system units, but here goes:
Convert density from pounds per cubic foot to pounds per cubic inch by dividing 655/1728, which is appx 0.4 lb/in^3. Now, find the max. no of cubic inches, divide 2.5 lb by 0.4 lb/in^3, to get 10 in^3 appx. Now you can find the height of the pyramid: 10 = 4 (h/3), h is about 7 inches. Note, that's actually a very skinny pyramid.

Answer 3

you need the pyramid to weigh 2.5/655ft^3 so find the slant height by using the area of a pyramid equation using 2.5/655 and what the equation equals....anyway the answer is:

1 times the square root of 2

Answer 4

1 cubic foot = 1728 cubic inches has mass 655 pounds
1 cubic inches has mass 0.37905092592592592592592592592593 pounds
Let the height is h.
The volume is 4h cubic inches, the mass is 1.5162037037037037037037037037037h pounds= 2.5 pounds
h = 2.5/1.5162037037037037037037037037037 = 1.6488549618320610687022900763366 inches.

Answer 5

1 cu foot = 1728 cu inches

655 / 1728 = .38 lbs per cu inch

2.5 lbs / .38 = 6.58 cu in (max vol of the pyramid)

Given your pyramid has a base of 4 sq inches, make a pyramid with a flat top of 2 sq inches, the height cannot exceed: 2.23 inches.

That's your ticket!

Answer 6

(2.5 lb)(1 ft^3 / 655 lb)(1728 in^3/1 ft^3) = 6.595420 in^3 = (1/3)(4 in^2)h
h ≤ 4.946565 inches

Answer 7

it depends on the construction material the Egyptians seem to prefer a 45 degree slope for the heavy stone blocks they used

Answer 8

the answer is I think: 0.008587786259541984732824427480916 in.

However I am not sure. I think the density you gave for silver may be wrong but again I do not know.

Answer 9

1/sqrt(2)