Question 1193436
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The weight is proportional to the volume; the distance from the vertex is a linear measurement.  So, given similar figures, the ratio of heights is the cube root of the ratio of volumes.<br>
To get a pyramid with 1/3 the volume of the whole pyramid, the height of the pyramid needs to be (cube root of 1/3) times the volume of the whole pyramid:<br>
{{{(1/3)^(1/3)}}} = 0.69336 to 5 decimal places.<br>
To get a pyramid with 2/3 the volume of the whole pyramid, the height of the pyramid needs to be (cube root of 2/3) times the volume of the whole pyramid:<br>
{{{(2/3)^(1/3)}}} = 0.87538 to 5 decimal places.<br>
ANSWER: To get three pieces with the same weight, the two planes cutting the pyramid of height h parallel to the base should be at distances 0.69336h and 0.87538h from the vertex.<br>