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Free_Kalibri [48]
2 years ago
15

A pyramid with a square base is cut by a plane that is parallel to its base and is 2 units from the base. The surface area of th

e smaller pyramid that is cut from the top is half the surface area of the original pyramid. What is the altitude of the original pyramid
Mathematics
1 answer:
icang [17]2 years ago
7 0

Answer:

  6.83 units

Step-by-step explanation:

Let the height of the original pyramid be represented by h. Then the cut off top has a height of (h -2). The scale factor for the area is the square of the scale factor for height, so we have ...

  (height ratio)^2 = 1/2

  ((h -2)/h)^2 = 1/2

  (h -2)√2 = h . . . . . . square root; multiply by h√2

  h(√2 -1) = 2√2 . . . . add 2√2 -h

  h = (2√2)/(√2 -1) ≈ 6.8284 . . . units

The altitude of the original pyramid is about 6.83 units.

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