Question : A solid copper sphere of radius 9 cm is hammered and moulded into a wire of radius 2 cm. What is the length of this wire?
Option 1: 224 cm
Option 2: 183 cm
Option 3: 198 cm
Option 4: 243 cm
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Correct Answer: 243 cm
Solution :
Radius of sphere, $r_1$ = 9 cm
Radius of wire, $r_2$ = 2 cm
Let the length of the wire be $h$.
Volume of sphere = $\frac{4}{3} \pi r_1^3$
Volume of cylindrical wire = $\pi r_2^2 h$
Now, volume of sphere = volume of cylindrical wire
⇒ $\frac{4}{3} \pi r_1^3 = \pi r_2^2 h$
⇒ $\frac{4}{3}\times 9^3 = 2^2\times h$
⇒ $h=243$ cm
Hence, the correct answer is 243 cm.
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