Question : A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 mm. Find the length of the wire.
Option 1: 143 m
Option 2: 108 m
Option 3: 324 m
Option 4: 234 m
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Correct Answer: 108 m
Solution :
Diameter of sphere = 18 cm
Radius of sphere, $R$ = 9 cm
Diameter of wire = 6 mm
The radius of wire, $r$ = 3 mm = 0.3 cm
Let $l$ be the length of the wire.
Volume of sphere = volume of wire
$\frac{4}{3}\pi R^3 = \pi r^2l$
$\frac{4}{3}×9^3 = 0.3^2l$
$l = \frac{4×729}{3×0.09}=10800$ cm $=108$ m
Hence, the correct answer is 108 m.
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