SOLUTION: The great pyramid in Egypt today is 138.8 meters tall and has a volume of 2.20 million cubic meters. A company plans to make clay replicas of the Pyramid to scale with the height 3

Question 1062192: The great pyramid in Egypt today is 138.8 meters tall and has a volume of 2.20 million cubic meters. A company plans to make clay replicas of the Pyramid to scale with the height 32 centimeters. How much clay will they need per pyramid?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the ratio of the volume is equal to the cube of the ratio of the height.

so, if the height of the pyramid is 138.8 meters, and the height of the clay model is .32 meters, then the ratio of the height of the model to the height of the pyramid is equal to .32 / 138.8.

the ratio of the volume of the model to the volume of the pyramid should therefore be equal to (.32 / 138.8)^3.

since the volume of the pyramid is 2.2 million cubic meters, then the volume of the clay model should be equal to 2.2 * 10^6 * (.32 / 138.8)^3 cubic meters.

that would make it equal to .0269590272 cubic meters.

i confirmed by using an online calculator.

first i determined that each side of the square base of the original pyramid have to be equal to 218.0606161 meters.

the volume of the original pyramid is therefore equal to 1/3 * 138.8 * (218.0606161)^2 which is equal to 2,200,000 cubic meters.

i then reduced each side of the original pyramid by the ratio of (.32/138.8) to get height = .32 meters and side length of the base = .5027334088 meters.

the volume of the clay model is equal to 1/3 * .32 * (.5027334088)^2 = .0269590272 cubic meters.

the ratio of the height of the model to the height of the pyramid is equal to .32 / 138.8 = .0023054755.

the ratio of the volume of the model to the volume of the pyramid is equal to .0269590272 / 2,200,000 = 1.225410329 * 10^-8.

if you take the cube of .0023054755, you will get 1.225410329 * 10^-8.

this confirms the ratio is correct.

the ratio of the volume is equal to the ratio of the height cubed.

here are the results of the online calculator

the first is the original pyramid.

the second is the model.

$$$

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