Question : A solid metallic sphere of radius 9 cm is melted and recasted into a wire of radius 2 cm. What is the length of the wire?
Option 1: 343 cm
Option 2: 152 cm
Option 3: 243 cm
Option 4: 184 cm
Correct Answer: 243 cm
Solution :
Given,
A solid metallic sphere of radius 9 cm is melted and recast into a wire of radius 2 cm.
We know, The volume of a sphere = $\frac43πr^3$, where $r$ is the radius
And, the Volume of a wire = $πr^2l$, where $l$ is its length.
⇒ Volume of the sphere $=\frac43\pi ×9^3= 972\pi $ cm
3
⇒ Volume of the wire $=\pi(2)^2l=4\pi l$ cm
3
The volume will remain the same
$972 × \pi = 4 × \pi × l$
⇒ $l=\frac{972}{4}$
⇒ $l=243$ cm
Hence, the correct answer is 243 cm.
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