Question

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Answer 1

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

Answer 2

Answer:

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