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Two solid right circular cones have the same height. The radii of their bases are \(a\) and \(b\). They are melted and recast into a cylinder of same height. The radius of the base of the cylinder is ______ ?

 Jan 31, 2021
 #1
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Volume  of first cone =  pi (a)^2  h  /  3

 

Volume of second cone =  pi (b^2) h  / 3

 

So

 

Volume  of   cylinder  =  combined volumes of  cones   =   pi * h ( a^2  + b^2)  / 3

 

So

 

pi * r^2 *  h    =   pi * h ( a^2 + b^2)  /  3

 

r^2  =   (a^2 +b^2)   / 3

 

r  =   sqrt  [  (a^2 +b^2) / 3  ]   =    radius of  the  cylinder

 

cool cool cool

 Jan 31, 2021

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