 # Height of a cone is 60 cm. A small cone is cut off by a plane parallel to the base and it's volume is 1/64 th of the volume of the original cone. The height from the base at which the section is made is?

11 years ago

dear akshay,

Let h1 and r1 be the height and radius of the base of the smaller cone and h2 ( = 60 cm ) and r2be the height and radius of the bigger cone. here h1 / h2 = r1 / r2. ( Similar triangles )   ----- ( 1 )

Now according to the question

( (1 /3 ) pai* r1 2 h1 )  /  (( 1/3) pai * r2 2 h2 )      =1 / 64

r1 2*h1 / r2 2*h2 = 1 / 64         h1 3 /  h2 3  =  1 / 64                  ( by applying relation   1 )

h1 / h = 1 / 4  or h1 / 60  =  1 /  4          ( since h2 = 60 )

or h1 =  15 cm.          There the height from the base at which the section is made =  60 - 15  = 45 cm.Let h1 and r1 be the height and radius of the base of the smaller cone and h2 ( = 60 cm ) and r2be the height and radius of the bigger cone. here h1 / h2 = r1 / r2. ( Similar triangles )   ----- ( 1 )

Now according to the question

( (1 /3 ) pai* r1 2 h1 )  /  (( 1/3) pai * r2 2 h2 )      =1 / 64

r1 2*h1 / r2 2*h2 = 1 / 64         h1 3 /  h2 3  =  1 / 64                  ( by applying relation   1 )

h1 / h = 1 / 4  or h1 / 60  =  1 /  4          ( since h2 = 60 )

or h1 =  15 cm.          There the height from the base at which the section is made =  60 - 15  = 45 cm.

BEST OF LUCK..!!!!

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AMAN BANSAL

11 years ago