From.each end of a solid.metal cylinder metal was scooped out in the hemispherical form of same diameter. the heighy of the cylinder is 10 cm and base radius is 4.2 cm. the rst of the cylinder is melted and converter into a cylindrical wire of 1.4 cm thick ness. find the length of wire.
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Volume of metal cylinder = π × (4.2)^2 × 10
= 176.4π
Volume of two hemispheres =2 × 2/3×π×(4.2)^3
= 98.8π
Volume of cylinder melted = 176.4π - 98.8π
= 77.6π
Let H be the length of cylindrical wire,
π × (1.4 / 2)^2 × H = 77.6π
H = 158.36 cm
= 176.4π
Volume of two hemispheres =2 × 2/3×π×(4.2)^3
= 98.8π
Volume of cylinder melted = 176.4π - 98.8π
= 77.6π
Let H be the length of cylindrical wire,
π × (1.4 / 2)^2 × H = 77.6π
H = 158.36 cm
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Therefore the length of the wire is 158.4 cm
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