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 1/27 of the volume of the given cone,then what is the height above the base at which the section is made?

Consider a cone of cone of radius R and H . Let a cone of height h is cut off from the top of this cone whose base is parallel to the original cone. Let the radius of the cone that cut off from the original cone be r .


 
Now, PQ = H h = 30 cm – 10 cm = 20 cm
 
Thus, the section of the cone is mode at a height of 20 cm above the base.
Hope! This will help you.
Cheers!

  • 374

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

  • 31

Consider a cone of cone of radius R and H . Let a cone of height h is cut off from the top of this cone whose base is parallel to the original cone. Let the radius of the cone that cut off from the original cone be r .


 
Now, PQ = H h = 30 cm – 10 cm = 20 cm
 
Thus, the section of the cone is mode at a height of 20 cm above the base.
Hope! This will help you.
Cheers!
  • 59

1. Let the height of the cone formed by cutting the plane be h

Initial height of the cone(H)=30  cm

Let the radius of the base be R and that of the cut cone be r.

Since the triangle ADE and triangle ABC are similar hence,

Now,

 

Therefore height from the base where the plane is cut,

= 30-10

=20 cm

  • 75
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