<PRE><B>Question 1158312</B>
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I didn&#39;t follow all of the calculations in the solution shown by the other tutor....  But his answer is correct.&lt;br&gt;
HOWEVER, he did WAY too much work getting the answer.&lt;br&gt;
Here is a much easier way, using a basic principle of similar figures.&lt;br&gt;
The top cone and the original cone are similar figures.&lt;br&gt;
The ratio of the area of the cross section (base of the top cone) to the area of the base of the cone is 30:67.5 = 60:135 = 4:9 = 2^2:3^2.&lt;br&gt;
That means the scale factor between the top cone and the original cone is 2:3, and the ratio between the volumes of the two cones is 8:27.&lt;br&gt;
That in turn means the ratio of the volume of the top cone to the volume of the frustum is 8:19.&lt;br&gt;
ANSWER: 8:19&lt;br&gt;
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