Q. 165.0( 3 Votes )

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

Answer :

Let’s suppose the smaller cone have the radius r and height h cm


And radius of the given cone be R cm


Height of the original cone = 30cm



In triangle ∆OAB and ∆OCD


COD = AOB (common angle)


OCD = OAB (90°)


؞ ∆ OAB ∆OCD [ by A-A criteria]


Then,



………..(i)


Volume of small cone = volume of original cone



From equation (i)





h3 = 1000


h = 10cm


Height of the small cone = 10cm


AC = OA-OC


AC = 30-10 = 20


Hence selection has been made at height of 20cm above the base.


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