Expert: Richard J. Raridon - 8/8/2006

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.

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


I understand that the answer is: to buy enough paint to cover 13,663.7cm^2...
Can you help me understand how to get to this answer??

Answer
First of all, your scale is 300:1 so you divide each dimension by 300 to get the size of your model.  The base is 71.5cm on each side, a height of 47.8cm high and a slant height of 59.8cm.  The area of the sides of a pyramid = (1/2)(perimeter of base)(slant height) =
(1/2)(4*71.5)(59.8) = 8551.4 cm^2.  If you want to paint the bottom also, you add (71.5)^2 or 5112.25 cm^2