A metallic sphere of diameter 1cm is to be melted & recasted into a hollow sphere of thickness 1mm. Find the internal & external radii of the sphere.

Asked by araima2001 | 23rd Nov, 2015, 10:26: AM

Expert Answer:

begin mathsize 14px style Given colon Diameter space of space solid space sphere space equals space 1 space cm space therefore Radius space of space solid space sphere space equals space 0.5 space cm equals space 5 space mm Volume space of space solid space sphere space equals space 4 over 3 straight pi space straight r cubed equals space 4 over 3 straight pi space 5 cubed space space space... left parenthesis 1 right parenthesis Let space straight r subscript 1 space be space internal space radius space of space hollow space sphere Let space straight r subscript 2 space be space external space radius space of space hollow space sphere As space per space the space given space information comma space straight r subscript 2 space minus straight r subscript 1 space equals space 1 space mm space space therefore straight r subscript 2 space equals space straight r subscript 1 plus 1 space space space... space left parenthesis 2 right parenthesis Volume space of space hollow space sphere space equals space 4 over 3 straight pi space straight r subscript 2 cubed space minus space 4 over 3 straight pi space straight r subscript 1 cubed space Here space Volume space of space solid space sphere space equals Volume space of space hollow space space sphere space therefore 4 over 3 straight pi space 5 cubed space equals space 4 over 3 straight pi space straight r subscript 2 cubed space minus space 4 over 3 straight pi space straight r subscript 1 cubed space therefore 4 over 3 straight pi space 5 cubed space equals space space 4 over 3 straight pi open parentheses straight r subscript 2 cubed space minus straight r subscript 1 cubed space close parentheses therefore 125 space equals space open parentheses straight r subscript 2 cubed space minus straight r subscript 1 cubed space close parentheses therefore open parentheses straight r subscript 2 space minus space straight r subscript 1 close parentheses space open parentheses straight r subscript 2 squared plus straight r subscript 1 straight r subscript 2 plus straight r subscript 1 squared close parentheses equals space 125 space space space space Substituting space straight r subscript 2 space minus straight r subscript 1 space equals space 1 comma therefore space open parentheses straight r subscript 2 squared plus straight r subscript 1 straight r subscript 2 plus straight r subscript 1 squared close parentheses equals space 125 space space space... left parenthesis 3 right parenthesis space Substituting comma straight r subscript 2 space equals space straight r subscript 1 plus 1 space in open parentheses 3 close parentheses space space space space end style
 
begin mathsize 14px style therefore space space open parentheses space straight r subscript 1 plus 1 close parentheses squared plus straight r subscript 1 open parentheses straight r subscript 1 plus 1 close parentheses plus straight r subscript 1 squared space equals space 125 therefore straight r subscript 1 squared plus 2 straight r subscript 1 plus 1 plus straight r subscript 1 squared plus straight r subscript 1 plus straight r subscript 1 squared space equals space 125 therefore 3 straight r subscript 1 squared space plus 3 straight r subscript 1 plus 1 equals 125 therefore 3 straight r subscript 1 squared space plus 3 straight r subscript 1 minus 124 space equals space 0 therefore straight r subscript 1 space equals 5.9 space or space minus space 6.9 Radius space can space not space be space negative therefore straight r subscript 1 equals Internal space radius space equals space 5.9 space mm straight r subscript 2 space equals External space radius space equals straight r subscript 1 plus 1 space equals 5.9 plus 1 equals space 6.9 space mm end style

Answered by Priti Shah | 23rd Nov, 2015, 02:28: PM

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