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Three solid metal spheres of radii 3 cm, 4 cm, 5 cm respectively, are melted together. The metal is recast as a single solid sphere. Find the percentage reduction in the area of surface resulting from this.

Option 1 -

0%

Option 2 -

16%   

Option 3 -

28%

Option 4 -

32%

0 2 Views | Posted a month ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    a month ago
    Correct Option - 3


    Detailed Solution:

    Let R be the radius of the recast sphere

    43πR3=43π (33+43+53)

    R3 = 216 ⇒ R = 6

    Total surface area of 3 spheres

    =4π (32+42+52)=4π×50=200π 

    Surface area of the recast sphere = 4π (62)=144

    % reduction in area = (200π−144π)200π×100%=28%

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