Q. 65.0( 1 Vote )

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be    of the volume of the given cone, at what height above the base is the section made.

Let the height of the original cone (H) = 30 cm
∴Volume of the original cone = R2
= R2 x 30 = 10R2
Volume of the small cone( r2h) = of Volume of the original cone     | h = height of small cone
⇒  r2h = R ⇒  h =      ........(i)
Since     ΔADE ~ ΔABC (BC Il DE)
...........(ii)
From Eqs (i) and (ii) we get
h =
h = 10 cm.
... Height above the base = 30 - 10 = 20 cm.

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