SOLUTION: a wooden pyramid is to be cut into 2 parts of equal weights by a plane parallel to its base. find the ratio of the heights of the two parts

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Question 1085826: a wooden pyramid is to be cut into 2 parts of equal weights by a plane parallel to its base. find the ratio of the heights of the two parts
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A wooden pyramid is to be cut into 2 parts of equal weights by a plane parallel to its base.
Find the ratio of the heights of the two parts.
:
Use an example the original pyramid: base = 100 sq/units, height = 12 unit
1%2F3*100*12 = 400 cu/units
By what percent x,(decimal form) do we have to reduce the base area and height to get a vol of 200 cu/units
1%2F3*100x * 12x = 200
%281200x%5E2%29%2F3 = 200
400x^2 = 200
x^2 = 200%2F400
x^2 = .5
x = sqrt%28.5%29
x = .707
check the half pyramid vol
1%2F3.707(100) * .707(12) =
%2870.7+%2A+8.485%29%2F3 = 199.97 ~ 200
:
Ratio of the heights 1:707