A metal spherical shaped ball, with a radius of 6 cm needs to be melted and converted into a wire of diameter 2 mm. The maximum length of the wire produced can be ____ m.

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A metal spherical shaped ball, with a radius of 6 cm needs to be melted and converted into a wire of diameter 2 mm. The maximum length of the wire produced can be 36 m.It is given that a metal spherical shaped ball, with a radius of 6 cm needs to be melted and converted into a wire of diameter 2 mm.We know that the volume of the sphere is

4
    3
   
   π
    r
    3
   
   ,
   where r is the radius of the sphere. The volume of the cylinder is

π
    r
    2
   
   h,
   where r is the radius of the cylinder and h is the height of the cylinder.Since the diameter of a sphere is 6 cm, the radius of the sphere is,

6
    2
   
   =3 cm.
  Similarly, since the diameter of the wire is 2 mm, so radius of the wire is,

2 mm
      2
     
     =1 mm

=0.1 cm

Let the length of the wire be h cm.Then, we can calculate the height of the wire as,

π×
      
       r
      
      2
     
     ×h=
      4
      3
     
     ×π×
      
       R
      
      3

⇒π×

0.1
      
      2
     
     ×h=
      4
      3
     
     ×π×
      
       3
      
      2

⇒h=

4
        3
       
       ×π×27
      
       π×

0.1
         
        2

⇒h=

4×9
        
         0.01

cm

⇒h=3600 cm

⇒h=36 m

Therefore the maximum length of the wire is 36 m.

A metal spherical shaped ball, with a radius of 6 cm needs to be melted and converted into a wire of diameter 2 mm. The maximum length of the wire produced can be ____ m.

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