Question
Mon March 09, 2015 By: R K Jha

A spherical ball of lead, 3 cm in diameter is melted and recasted into three different sized spherical balls. Find the diameter of the third ball if the diameter of the first two balls are 1 cm and 1.25 cm.

Expert Reply
Prasenjit Paul
Tue March 10, 2015
L e t space t h e space r a d i u s space o f space t h e space t h i r d space b a l l space b e space apostrophe r apostrophe 4 over 3 straight pi open parentheses 3 over 2 close parentheses cubed equals 4 over 3 straight pi open parentheses 1 half close parentheses cubed plus 4 over 3 straight pi open parentheses fraction numerator 1.25 over denominator 2 end fraction close parentheses cubed plus 4 over 3 straight pi open parentheses straight r close parentheses cubed rightwards double arrow open parentheses 3 over 2 close parentheses cubed equals open parentheses 1 half close parentheses cubed plus open parentheses fraction numerator 1.25 over denominator 2 end fraction close parentheses cubed plus open parentheses straight r close parentheses cubed space space space space space left square bracket Removing space 4 over 3 straight pi space from space both space sides right square bracket rightwards double arrow open parentheses 3 over 2 close parentheses cubed minus open parentheses 1 half close parentheses cubed minus open parentheses fraction numerator 1.25 over denominator 2 end fraction close parentheses cubed equals straight r cubed rightwards double arrow straight r cubed equals open parentheses 3 over 2 close parentheses cubed minus open parentheses 1 half close parentheses cubed minus open parentheses fraction numerator 1.25 over denominator 2 end fraction close parentheses cubed rightwards double arrow straight r cubed equals fraction numerator 3 cubed minus 1 minus open parentheses 1.25 close parentheses cubed over denominator 8 end fraction rightwards double arrow straight r cubed equals fraction numerator left parenthesis 3 minus 1.25 right parenthesis left parenthesis 3 squared plus 3 cross times 1.25 plus 1.25 squared right parenthesis minus 1 over denominator 8 end fraction rightwards double arrow straight r cubed equals fraction numerator 1.75 cross times open parentheses 9 plus 3.75 plus 1.5625 close parentheses minus 1 over denominator 8 end fraction rightwards double arrow straight r cubed equals fraction numerator 1.75 cross times 14.3125 minus 1 over denominator 8 end fraction rightwards double arrow straight r cubed equals fraction numerator 24.046875 over denominator 8 end fraction therefore straight r equals 2.89 Radius space of space the space third space ball space equals space 2.89 space cm
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