A solid metallic sphere of radius 9 cm is melted and recast into a wire of radius 2 cm. What is the length of the wire?
Answer & explanation
Correct answer: option 3
Volume of a sphere = \(\frac{4}{3}\)πr3,
Volume of a wire = πr2l, where 'l' is its length.
Volume of the sphere = \(\frac{4}{3}\)π(9)3=972π cm3
Volume of the wire = = π(2)2l = 4πl cm3
By equating volume of sphere and volume of wire we get,
972 × π = 4 × π × l
l = \(\frac{972}{4}\) = 243 cm