Question 1137150
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The small cone (which is the cut part of the large cone) is similar to the large cone.


The similarity coefficient (the ratio of corresponding linear dimensions) is  {{{2/3}}}   (counting smaller to larger).


It means that the smaller cone volume is  {{{(2/3)^3}}} = {{{8/27}}}  of the volume of the large cone.


Then the volume of the resulting frustum is  {{{1 - 8/27}}} = {{{(27-8)/27}}} = {{{19/27}}} of the volume of the large cone.


Thus the value under the question is  {{{54pi*(19/27)}}} = {{{38pi}}}.    <U>ANSWER</U>
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Solved.