A solid metallic cube of side 4.4 cm is melted and recast in the form of a wire of radius 2 mm. Find the length (in cm) of the wire. (Use $π = \frac{22}{7}$)

677.6

We know that,

Volume of cube = a³

Volume of cylinder = πr²h

Given,

Length of the edge, a = 4.4 cm

Radius = 2 mm = 0.2 cm

So,

Volume of the cube = (4.4)³ = 85.184 cm3 

Now, Volume of the wire = πr²h

\(\frac{22}{7}\)× 0.2² = \(\frac{0.88}{7}\)

We know that, Volume of the cube = volume of the wire 

So, Length of the wire = \(\frac{a^3}{ πr^2h }\)

\(\frac{85.184 × 7}{0.88}\) = \(\frac{596.288}{0.88 }\) = 677.6