What is the height of the scaled-up Pyramid of Egypt?

[powergirl]

My Dad has a miniature Pyramid of Egypt. It is 3 inches in height. Dad was invited to display it at an exhibition. Dad felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is (1/ 9) times the density of the material used for the miniature. He did a "back-of-the-envelope" calculation to check whether the model would be big enough.

If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid? Give your answer to two places of decimal.

 

[dontdisturbmycircles]

9 inches!

needed more text

 

[powergirl]

NO...Not right

 

[Hootenanny]

81"

(Again text limit)

 

[dextercioby]

27 inches ?

Daniel.

 

[dontdisturbmycircles]

How did you guys solve this? This one confused me for some reason. I know that all the dimensions between the two are proportional but I couldn't immediately see how to put that into the equations. A ratio would have worked but I didn't see one that helped solve the problem. I would sit down and think harder about it but I got to go.

 

[dontdisturbmycircles]

Yea, it's 27", I have no idea what the heck I was thinking. Was just about to fall asleep and then I realized.

 

[powergirl]

No one gave me the right ans:

 

[dontdisturbmycircles]

what the hell, this question is making me mad. lol

 

[powergirl]

try it.....

 

[Hootenanny]

6.24" text limit again[/color]

3\cdot\left(\frac{1}{9}\right)^{-1/3}

 

[neutrino]

6.24 it is.

 

[powergirl]

yes 6.24 is correct
soln is as:
Mass = Density x Volume; and
Volume of model / Volume of miniature = (H of model / H of miniature)3.


In the above equation, H is the characteristic dimension (say, height).

If the mass is to be the same, then density is inversely proportional to volume. Also, the volumes are directly proportional to the cubes of the heights for objects that are geometrically similar. Therefore, the heights are seen to be inversely proportional to the cube roots of the densities. Thus,

Height of model = Height of miniature x (Density of miniature / Density of model)1/3 or

Height of model = 3 x [ 91/3 ] = 6.24 inches.