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

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In summary, the conversation discusses how the speaker's dad built a scaled-up model of a miniature Pyramid of Egypt for an exhibition. By using a material with 1/9th the density of the original, the model was able to have the same mass as the miniature. Through a calculation using ratios and the relationship between density and volume, it was determined that the height of the scaled-up model would be 6.24 inches.
  • #1
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.
 
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  • #2
9 inches!

needed more text
 
  • #3
NO...Not right
 
  • #4
81"

(Again text limit)
 
  • #6
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.
 
  • #7
Yea, it's 27", I have no idea what the heck I was thinking. Was just about to fall asleep and then I realized.
 
  • #8
No one gave me the right ans:
 
  • #9
what the hell, this question is making me mad. lol
 
  • #10
try it.....
 
  • #11
6.24" text limit again

[tex]3\cdot\left(\frac{1}{9}\right)^{-1/3}[/tex]
 
Last edited:
  • #12
6.24 it is.
 
  • #13
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.
 

What is the Pyramid of Egypt?

The Pyramid of Egypt is a large, ancient structure located in Giza, Egypt. It is one of the oldest and most recognizable man-made structures in the world, built over 4,500 years ago as a tomb for the Egyptian Pharaoh Khufu.

How was the Pyramid of Egypt built?

The Pyramid of Egypt was built using large blocks of limestone and granite that were quarried and transported from nearby areas. The blocks were then shaped and stacked to create the pyramid shape. It is estimated that it took approximately 20 years and over 100,000 workers to complete the construction.

What is the significance of the Pyramid of Egypt?

The Pyramid of Egypt holds great cultural and historical significance as a symbol of ancient Egyptian civilization. It also serves as a testament to the advanced engineering and architectural capabilities of the ancient Egyptians.

How were the tombs inside the Pyramid of Egypt discovered?

The tombs inside the Pyramid of Egypt were discovered in ancient times, likely by looters searching for valuable treasures. The first recorded exploration of the interior of the pyramid was in 820 AD by the Arab caliph al-Ma'mun, who found the main burial chamber and several artifacts.

What is the current state of the Pyramid of Egypt?

The Pyramid of Egypt is still standing and has undergone various restoration and conservation efforts over the years. It is now a popular tourist destination and a UNESCO World Heritage Site. However, the pyramid's exterior and interior have suffered some damage from natural wear and tear as well as from human activity.

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