The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section.

Question:

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

Solution:

Radius of the copper sphere, = 9 cm
Length of the wire, = 108 m = 10800 cm
Volume of the sphere = volume of the wire
Suppose that r cm is the radius of the wire.

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

$\Rightarrow \frac{4}{3} \times 9^{3}=r^{2} \times 10800$

$\Rightarrow r^{2}=\frac{4 \times 729}{3 \times 10800}=\frac{4 \times 81}{3 \times 1200}=\frac{9}{100}$

$\Rightarrow r=\frac{3}{10}=0.3 \mathrm{~cm}$

∴ Diameter of the wire = 0.6 cm

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