Question

The height of a cone is 30cm. 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 1/27
the base is the section made?​

Answer 1

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Let the bigger cone be ABC and the smaller cone that is cut off the top be AFG.

Let the radius of the smaller cone be = r, and the height = h

and the radius of the bigger cone be = R, and the height = 30 cm (given)

Consider the triangle ADG and AEC

0 each)

 

so triangle ADG is similar to triangle AEC

=> AD/AE = DG/EC

=> h/30 = r/R ........................(1)

Also, Volume of the smaller cone = 1/27 (volume of bigger cone)

(1/3) pi r2 h = (1/27)(1/3) pi R2 (30)

h/30 = R2 /27r2 ..............(2)

from (1) and (2)

r/R = R2/27r2

27r3 = R3

=> R = 3r

Substituting the value of R in (1)

h/30 = r/3r

=> h = 30/3

=> h = 10

So, the height at which the section is made = 30 - 10 = 20 cm

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Answer 2

Step-by-step explanation:

hope it helps u......❣️