please answer

Asked by nmenghani | 13th Jan, 2010, 10:32: AM

Expert Answer:

Let R, H be the radius and height of given cone and r, h be the radius and height of cut off cone.

and V, v be their respective volumes,

V = πR2H/3 and v = πr2h/3

v = V/27

πr2h/3 = πR2H/(3x27)

r2h = R2H/27 .............(1)

Let y be the height for a location to cut off cone.

y + h = H

and r/R = h/H

r = hR/H

Using these in (1),

h3R2/H2 =  R2H/27

h3 = H3/27

h = H/3

y + h = H

y = H - h

= H - H/3

y =2H/3

Hence the cone is cut off at a height 2/3 of the total height from bottom.

Regards,

Team,

TopperLearning.

 

 

Answered by  | 13th Jan, 2010, 10:53: AM

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