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From each end of a solid metal cylinder,metal was scooped out in hemispherical form of same diameter.The height of cylinder is 10cmand r = 4.2cm.The rest

of the cylinder is melted and turned into a cylindrical wire of 1.4cm thickness.find length of wire.


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.

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