Question

the height of a cone is 60cm a small cone is cut off at the top by a plane parallel to the bases and its volume is 1/64 the original cone . find the height from the base at which the section is made

Answer 1

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 / h2  = 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 / h2  = 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..!!!!