# 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?

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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