Question 73

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:

Solution

Volume of lead = 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$$^3$$

$$\Rightarrow$$  $$\pi\ r^2h=3960$$

$$\Rightarrow$$  $$\frac{22}{7}\left(0.3\right)^2h=3960$$

$$\Rightarrow$$  $$\frac{1}{7}\left(0.3\right)^2h=180$$

$$\Rightarrow$$  $$h=\frac{180\times7}{0.3\times0.3}$$

$$\Rightarrow$$  $$h=\frac{180\times7\times100}{3\times3}$$

$$\Rightarrow$$  $$h=14000$$ cm

$$\Rightarrow$$  $$h=140$$ m

$$\therefore\ $$Length of the cylindrical wire = 140 m

Hence, the correct answer is Option A


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