If 3.96 cubic dm of lead is to be drawn in to a cylindrical wire of diameter 0.6 cm, then the length of the wire (in metres), is:
Volume of lead =Â 3.96 dm$$^3$$ = 3.96 x (100 cm)$$^3$$ = 3960 cm$$^3$$
Given, diameter of the cylindrical wire = 0.6 cm
$$\Rightarrow$$ Radius of the cylindrical wire = 0.3 cm
Let the length of the cylindrical wire = $$h$$
According to the problem,
Volume of the cylindrical wire = 3960 cm$$^3$$
$$\Rightarrow$$ Â $$\pi\ r^2h=3960$$
$$\Rightarrow$$ Â $$\frac{22}{7}\left(0.3\right)^2h=3960$$
$$\Rightarrow$$ Â $$\frac{1}{7}\left(0.3\right)^2h=180$$
$$\Rightarrow$$ Â $$h=\frac{180\times7}{0.3\times0.3}$$
$$\Rightarrow$$ Â $$h=\frac{180\times7\times100}{3\times3}$$
$$\Rightarrow$$ Â $$h=14000$$ cm
$$\Rightarrow$$ Â $$h=140$$ m
$$\therefore\ $$Length of the cylindrical wire = 140 m
Hence, the correct answer is Option A
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