Cutting cone

A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.

Correct result:

x =  2.4756 cm

Solution:

r=10 cm h=12 cm  V1=π r2 h=3.1416 102 123769.9112 cm3 V2=V1/2=3769.9112/21884.9556 cm3  r2:h2=r:h V2=π r22 h2 V2=π (r/h h2)2 h2  h2=V2 h2π r23=1884.9556 1223.1416 10239.5244 cm  x=hh2=129.52442.4756=2.4756 cm   Verifying Solution:  r2=r/h h2=10/12 9.52447.937 cm V22=π r22 h2=3.1416 7.9372 9.52441884.9556 cm3



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