Question
Download Solution PDFA solid sphere of diameter 6 cm is melted and then cast into cylindrical wire of radius 0.3 cm. Find the length of the wire.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Diameter of the solid sphere = 6 cm
Radius of the solid sphere (r) = 6 cm / 2 = 3 cm
Radius of the cylindrical wire (R) = 0.3 cm
Formula used:
Volume of sphere = (4/3)πr3
Volume of cylinder = πR2h
Volume of sphere = Volume of cylinder
Calculation:
Volume of sphere = (4/3)π(3)3
⇒ Volume of sphere = (4/3)π(27) = 36π cm3
Volume of cylinder = π(0.3)2h
⇒ 36π = π(0.09)h
⇒ h = 36 / 0.09 = 400 cm
⇒ h = 4 m
∴ The correct answer is option (1).
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