SOLUTION: A cone of volume 54π is cut by a plane parallel to the base, one third of the way up the height of the cone (from the base). Find the volume of the resulting frustum.
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Question 1137150: A cone of volume 54π is cut by a plane parallel to the base, one third of the way up the height of the cone (from the base). Find the volume of the resulting frustum. Answer by ikleyn(52782) (Show Source):
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 (counting smaller to larger).
It means that the smaller cone volume is = of the volume of the large cone.
Then the volume of the resulting frustum is = = of the volume of the large cone.
Thus the value under the question is = . ANSWER
