<PRE><B>Question 1111892</B>
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The answer from the other tutor is not correct.  With a frustum (truncated pyramid), you can&#39;t just use the length of a side halfway between the two bases to find the volume of the frustum....&lt;br&gt;
Here are three ways to find the volume of the frustum and thus find its weight.&lt;br&gt;
(1) Consider the frustum as a truncated hexagonal pyramid; find the volume of the original pyramid and subtract off the volume of the pyramid that was cut off.&lt;br&gt;
Use similar triangles to find the height h of the original pyramid:
{{{(h-16)/16 = h/29}}}
{{{29h-464 = 16h}}}
{{{13h = 464}}}
{{{h = 464/13}}}&lt;br&gt;
The volume of the original pyramid is one-third the area of the base, times the height; the area of the regular hexagonal base is the area of 6 equilateral triangles with side length 29:
{{{V = (1/3)(6*29^2*sqrt(3)/4)*(464/13) = 25995.6844}}}&lt;br&gt;
The volume of the pyramid that is cut off is one-third the area of the base, times the height:
{{{V = (1/3)(6*16^2*sqrt(3)/4)*(464/13-16) = 4365.834}}}&lt;br&gt;
The volume of the frustum is the difference between the volumes of the two pyramids:
{{{V = 25995.6844-4365.834 - 21629.85}}}&lt;br&gt;
(2) In that first method, we found the volume of the pyramid that was cut off directly, using the formula for the volume of a pyramid.  We can also find the volume of that pyramid using the fact that the original pyramid and the pyramid that was cut off are similar figures.&lt;br&gt;
The scale factor between the two pyramids is 16:29; the ratio of the volumes of the two pyramids is (16:29)^3.&lt;br&gt;
So the volume of the frustum can be calculated as the volume of the original pyramid, multiplied by (1 - (16/29)^3):
{{{V = 25995.6844(1-(16/29)^3) = 21629.85}}}&lt;br&gt;
(3) There is a rather obscure formula for the volume of a frustum of a pyramid with a regular polygonal base; for a frustum with a regular hexagonal base, with base side lengths 29 and 16 and height 16, the formula is
{{{V = (1/3)((6*29^2*sqrt(3))/4+(6*29*16*sqrt(3))/4+(6*16^2*sqrt(3))/4)(16)}}}&lt;br&gt;
Evaluating this expression of course gives the same answer of 21629.85 for the volume of the frustum.&lt;br&gt;
That answer is in cubic feet; then to find the weight you simply multiply that by the density in pounds per cubic foot:
{{{21629.85*99 = 2141355}}}&lt;br&gt;
2,141,355 pounds -- a rather heavy chunk of something.
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