Question

The hieght 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,at what height above the base is the section cut​

Answer 1

Consider ∆ADC & ∆ AGF

They are similar ∆s

=> AD/DC = AG/GF

Let the radius of base & height of smaller cone be r & h respectively.

=> AG = h & GF = r

=> h/r = 30/3 = 10

=> h = 10r

Volume of small Cone = 1/3 πr^2h

= 1/3π r^2 x 10r

= 1/3 π x 10 x r^3

Now it is given that :

1/3 π x 10 x r^3 = 1/27 x 1/3π x 9 x 30

=> r^3 = 1 => r = 1

=> h = 10r = 10

So, the cone must be cut 30 - 10 = 20 cms from the base.

Answer 2

Answer:

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