The height of a cone is 40cm. A small cone is cut off at the top of a plane parallel to its base. If it's volume be 1/64 of the volume of given cone, at what height above the base is the second cut?
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let at x height we cut the given cone
now after cutting small cone form above big cone
radius of small cone =?
we use similar concept ,
40/(40-x)=R/r
r=(40-x)/40.R
now ,
volume of small cone =1/64 x volume of given cone
π{(40-x)/40}^2R^2(40-x)=1/64 x πR^2 x 40
(40-x)^3=40^3 /(4)^3
take both side cube root
(40-x)=40/4=10
x=30cm
hence at 30m above cut the cone
now after cutting small cone form above big cone
radius of small cone =?
we use similar concept ,
40/(40-x)=R/r
r=(40-x)/40.R
now ,
volume of small cone =1/64 x volume of given cone
π{(40-x)/40}^2R^2(40-x)=1/64 x πR^2 x 40
(40-x)^3=40^3 /(4)^3
take both side cube root
(40-x)=40/4=10
x=30cm
hence at 30m above cut the cone
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