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The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm.

Question:

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.

Solution:

Given that

Diameter of sphere = 6 cm

Radius of sphere = d/2 = 6/2 = 3 cm = r1

Diameter of the wire = 0.2 cm

Radius of the wire = 0.1 cm = r2

Volume of sphere = Volume of wire

$\frac{4}{3} \pi r_{1}^{3}=\pi r_{2}^{2} h$

$=\frac{4}{3} \times 3 \times 3 \times 3=0.1 \times 0.1 \times \mathrm{h}$

$h=\frac{4 \times 3 \times 3}{0.1 \times 0.1}$

h = 3600 cm

h = 36 m

Therefore length of wire = 36 m

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