The diameter of a sphere is 6 cm.

Question:

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire

Solution:

Let the length of the wire be h cm.
Radius of the wire, = 1 mm = 0.1 cm
Radius of the sphere, R = 3 cm
Now, volume of the sphere = volume of the cylindrical wire

$\Rightarrow \frac{4}{3} \pi R^{3}=\pi r^{2} h$

$\Rightarrow 4 \times 3^{2}=(0.1)^{2} \times h$

$\Rightarrow h=\frac{4 \times 9}{0.1 \times 0.1}=3600 \mathrm{~cm}=36 \mathrm{~m}$

∴ Length of the wire = 36 m

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