Question : A copper sphere of diameter 18 m is drawn into a cylindrical wire of length 12 m. What is the radius of the wire?
Option 1: 5 m
Option 2: 9 m
Option 3: 3 m
Option 4: 12 m
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Correct Answer: 9 m
Solution :
Diameter of copper sphere = 18 m
Radius ($R$) = $\frac{18}{2}$ = 9 m
Volume of copper sphere = $\frac{4}{3}×\pi×R^3$
= $\frac{4}{3}×\pi×9^3$ = $972\pi$
Since the volume is the same,
Volume of cylinder wire = $\pi r^2h$
⇒ $972\pi = \pi×r^2×12$
⇒ $r^2 = \frac{972}{12} =$ 81
⇒ $r = 9$
Hence, the correct answer is 9 m.
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