Question
Wed March 18, 2015 By: Jerlin George

Two spheres of same metal weight 1kg and 7kg with the smaller sphere having a radius of 3 cm are recast into a big sphere. Find the radius of the recasted sphere.

Expert Reply
Vimala Ramamurthy
Fri March 20, 2015
Total weight of recasted sphere is 1kg+7kg=8kg
Radius of the small metal 'r'=3 cm.
Hence, density of the metal
fraction numerator 1 space k g over denominator begin display style 4 over 3 end style πr cubed end fraction equals begin inline style fraction numerator 3 over denominator 4 cross times straight pi cross times 27 end fraction end style equals fraction numerator 1 over denominator 36 straight pi end fraction bevelled fraction numerator k g over denominator c m cubed end fraction
Let the radius of the recasted metal be 'R'.
8 equals fraction numerator 1 over denominator 36 straight pi end fraction bevelled fraction numerator k g over denominator c m cubed space cross times space begin display style 4 over 3 end style πR cubed end fraction rightwards double arrow straight R cubed equals 216 rightwards double arrow straight R equals 6 space cm
 
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