A structure which has a square base and four triangular sides meeting at a point is called pyramid.
At distance of 3.97 feet from its vertex , pyramid is cut by plane so that the two solids of equal weight will be formed.
<u>It is assumed that weight of pyramid is proportional to its volume.</u>
So,
, where V is volume of original pyramid and v is volume of small pyramid and k is constant.
Let us consider that at h distance, pyramid is cut from its vertex. So a small pyramid is also formed.
Assume that base area of original pyramid is A and base of small pyramid is a.
Volume of original pyramid is, 
So, weight of original pyramid, 
Volume of small pyramid is, 
So, weight of small pyramid, 
<u>Since, base and height of small pyramid and original pyramid are in proportion.</u>
So, 

Substituting value of a in equation 
So, 

Since,
, substitute in above equation.
So, ![800*\frac{h^{3} }{125}=400\\\\h^{3}=\frac{125}{2}\\\\h=\sqrt[\frac{1}{3} ]{62.5}\\\\h=3.97 feet](https://tex.z-dn.net/?f=800%2A%5Cfrac%7Bh%5E%7B3%7D%20%7D%7B125%7D%3D400%5C%5C%5C%5Ch%5E%7B3%7D%3D%5Cfrac%7B125%7D%7B2%7D%5C%5C%5C%5Ch%3D%5Csqrt%5B%5Cfrac%7B1%7D%7B3%7D%20%5D%7B62.5%7D%5C%5C%5C%5Ch%3D3.97%20feet)
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