The length of a wire (in cm) of 0.1 mm radius that can be drawn from melting a solid copper sphere of diameter 6 cm is:
Answer & explanation
Correct answer: option 2
We know that,
Volume of cylinder = πr2l
r = radius of wire
l = length of wire
Volume of solid sphere = \(\frac{4}{3}\)πR3
R = Radius of the solid sphere
We have,
Radius of wire (r) = 0.1 mm
Diameter of solid copper sphere (D) = 6 cm
Volume of solid sphere = \(\frac{4}{3}\) × 3.14 × 3 × 3 × 3 = 113.04 cm3
Volume of wire = 3.14 × \(\frac{1}{100}\) × \(\frac{1}{100}\) × l
We know that,
Volume of wire = Volume of solid sphere
3.14 × \(\frac{1}{100}\) × \(\frac{1}{100}\) × l = 113.04 cm3
= l = 360000 cm