The length of a wire (in m) of 0.5 mm radius that can be…

The length of a wire (in m) of 0.5 mm radius that can be drawn after melting a solid copper sphere of diameter 12 cm is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. 1152.

Radius of sphere R = 12/2 = 6 cm

Volume of sphere = $\frac{4}{3}\pi R^3$ = $\frac{4}{3}\pi 6^3$ = 288π cm³

Radius of wire r = 0.5 mm = 0.05 cm

Volume of wire = $\pi r^2L$ = $\pi (0.05)^2L$ = 0.0025πL

Equating volume:

0.0025πL = 288π

⇒ L = 288/0.025 = 115200 cm = 115200/100 = 1152 m

SSC Selection Post 2022 PYQ — Question 68