Question:
The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.
Solution:
Given that diameter of a copper sphere = 18 cm
Radius of the sphere = 9 cm
Length of the wire = 108 m = 10800 cm
Volume of cylinder = Volume of sphere
$\pi r_{1}^{2} h=\frac{4}{3} \pi r_{2}^{3}$
$r_{1}^{2} \times 10800=\frac{4}{3} \times 9 \times 9 \times 9$
$r_{1}^{2}=0.009$
r1 = 0.3 cm
Therefore Diameter = 2 × 0.3 = 0.6 cm
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