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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