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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?

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?

Grade:10

2 Answers

Aman Bansal
592 Points
10 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

 

R.G. LOKKESH
19 Points
10 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 / 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..!!!! We are all IITians and here to help you in your IIT JEE preparation. Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian. Now you score 5+15 POINTS by uploading your Pic and

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