text: A Solid Metallic Sphere of Diameter 8 Cm is Melted and Drawn into a Cylindrical Wire of Uniform Width. If the Length of the Wire is 12 M, Then Find Its Width. - Mathematics
  
  Sum
  
  A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width.
  
  Solution
  
  We have,
  
  Radius of the metallic sphere, R= 8/2 = 4  "cm" and
  
  Height of the cylindrical wire, h = 12 m = 1200 cm
  
  Let The radius cylindrical wire, h = 12 m = 1200 cm
  
  Let the radius of the base be r.
  
  Now,
  
  Volume of the cylindrical wire = Volume of the metallic sphere
  
  => pi"r"^2"h" = 4/3 pi"R"^3
  
  => "r"^2 = (4"R"^3)/(3"h")
  
  => "r"^2 = (4xx4xx4xx4)/(3xx1200)
  
  => "r"^2 = 16/225
  
  => "r" =sqrt(16/25)
  
  => "r" = 4/15  "cm"
  
  ∴ The width of the wire = 2r
  
  =2xx4/15
  
  =8/15 "cm"
  
  So, the width of the wire is 8/15 cm.
  
  Is there an error in this question or solution?
  
  APPEARS IN
  
  RS Aggarwal Secondary School Class 10 Maths
  Chapter 19 Volume and Surface Area of Solids
  Exercise | Q 27 | Page 915