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)

h^{3} = 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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