Expert: Richard J. Raridon - 7/20/2006

Question
Hi my name is Lauren, and I am 18. I am having difficulty answering
this question::::


The Khafre pyramid in Egypt has a square base that is 214.5 meters on
each side, a height of 143.5 meters, and a slant height of 179.4 meters.
You construct a scale model of the pyramid using a scale of 6 meters to
2 centimeters.

Question 1:
If you are painting the entire model, you should buy enough paint to
cover how many square centimeters?

Question 2:
How many times greater is the volume of the actual pyramid than the
volume of the model?

Thank you for your help!

Answer
So your model has a square base that is 71.5 cm on each side, a height of 47.83 cm, and a slant side of 59.8 cm.
1. The area of a pyramid is (1/2)(perimeter of base)(slant height) = (1/2)(4)(71.5)(59.8) = 8551.4 cm^2
2. Since the scale factor is 300, the actual pyramid has a volume equal to (300)^3 = 2.7x10^7 times the volume of the model