SOLUTION: A pyramid of Altitude 18 cm. is divided into three parts by two planes passed parallel to the base. These planes are at distances of 6cm. and 10 cm. from the vertex. Compute the ra

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Question 1188847: A pyramid of Altitude 18 cm. is divided into three parts by two planes passed parallel to the base. These planes are at distances of 6cm. and 10 cm. from the vertex. Compute the ratio of the volume of the upper most part to the volume of the lowest part. (Ans. 0.045)
Answer by ikleyn(52908) About Me  (Show Source):
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A pyramid of Altitude 18 cm. is divided into three parts by two planes passed parallel to the base.
These planes are at distances of 6cm. and 10 cm. from the vertex.
Compute the ratio of the volume of the upper most part to the volume of the lowest part. (Ans. 0.045)
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In this problem, you have three pyramids with the common vertex. 

They all are similar 3D bodies with the linear similarity coefficients  6 : 10 : 18.

Hence, their volumes are in the ratios  6%5E3 : 10%5E3 : 18%5E3, or  216 : 1000 : 5832.


So, you may think that the volume of the greatest pyramid is 5832x cubic units;

                       the volume of the smallest pyramid is 216x cubic units

                  and  the volume of the middle size pyramid is 1000x cubic units,

where x is some common measure of the three volumes.


The lowest part volume is then  5832x units MINUS 1000x units = 4832x units,

and the ratio under the problem's question is  216%2F4832 = 0.044702 = 0.045  (rounded).    ANSWER

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