From each end of a solid metal cylinder, metal was scooped out in hemispherical form of 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. [Use π=22/7]



First, we need to find out the volume of the previous solid metal cylinder.
h= 10 cm
r = 4.2 cm

Volume of cylinder before scooping out = πr²h
= 176.4π cm³

Volume of scooped part =
= 4/3 × π × (4.2)³
= 98.784π ≈ 98.8π cm³

Therefore volume of the scooped metal cylinder = 176.4π- 98.8π = 77.6π cm³

Now For wire,
Diameter = 1.4 cm
Radius = 1.4/2 = 0.7

The volume of the scooped metal cylinder = The volume of the wire
77.6π = πr²h
Cut π from both the sides
77.6 = (0.7)²h
h = 77.6/0.49
h = 158.36 cm ≈158.4 cm

Therefore, the length of the wire would be approximately 158.4 cm.