The radius of a solid metallic sphere is equal to 15 cm. It is melted and drawn into a long wire of radius 15 mm having uniform cross-section. Find the length of the wire.
Answer & explanation
Correct answer: option 4
We know that,
Volume of Sphere = \(\frac{4}{3}\)πr3
Volume of cylinder = πr²h
We have,
Radius = 15 cm.
It is melted and drawn into a long wire of radius 15 mm or 1.5 cm
According to the question,
Volume of sphere = Volume of cylinder
= \(\frac{4}{3}\)π × (15)3 = π × (1.5)2 × h
= \(\frac{4}{3}\) (3375) = (2.25) × h
= 4 × (1125) = (2.25) × h
= h = \(\frac{4500}{2.25}\) = 2000 cm