31. From each end of a solid metal cylinder, metal was scooped out in the hemispherical form of the same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire. ( π = 22/7)

Height of the solid metal cylinder, h = 10 cm
Radius of the solid metal cylinder, r = 4.2 cm

therefore,

Radius of each hemisphere = radius of the solid metal cylinder, r = 4.2 cm

Now, 

Volume of the rest of the cylinder = Volume of cylinder - 2 x volume of each hemisphere

 

Thickness of the cylindrical wire = 1.4 cm
Therefore, 
Radius of the cylindrical wire, R = 1.4/2 = 0.7 cm

Let the length of the wire be H cm.

It is given that the rest of the cylinder is melted and converted into a cylindrical wire.

therefore,

Volume of the cylindrical wire = Volume of the rest of the cylinder

⇒ π x 0.7 x 0.7 x H = π x (4.2)² x (4.4)



Hence, the length of the wire is 158.4 cm