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

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18 cm

15 cm

11 cm

10 cm

answer is D.

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Detailed Solution

Given that height of the cone is H=30cm.
Let the radius of the big and small cone be

R

and r .
It is also given that the volume of smaller cone is

127

of the given cone.
The volume of a cone is expressed as,

V = 13 π r 2 h

, where

r

and h be the radius and height of a cylinder.
The required figure is shown below,
Question Image

So,

V 2 V 1 = 127 ⇒ 13 π r 2 h 13 π R 2 H = 127 ⇒ 13 π r 2 h 13 π R 2 30 = 127 ⇒ r 2 h 30 R 2 = 127 ..... 1

From the figure,

⇒ r R = h 30

So, from the equation (1),
Question Image

Thus, the height is 10cm.
Therefore, option (4) is correct.

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