Question

please answer this question

Answer 1

Hey There,


Here, we have to understand one simple concept. The sphere is melted and then drawn into a wire. The shape changes. But, The Volume remains same. Thus, to find the answer, we simply equate initial volume to final volume.



For initial Sphere,

$Diameter = d = 6 \, \, cm \\ \\ \implies Radius = R= 3 \, \, cm = 3 \times 10^{-2} \, \, m$



For final Cylindrical Wire,

$Diameter = r = 2 \, \,mm \\ \\ \implies Radius=r= 1 \times 10^{-3} \, \,m \\ \\ \text{And let Length be } l$


Now, we equate the volumes in two cases:


$\text{Volume of sphere}=\text{Volume of wire} \\ \\ \\ \implies \frac{4}{3}\pi R^3 = \pi r^2 l \\ \\ \\ \implies l = \frac{4R^3}{3r^2} \\ \\ \\ \implies l = \frac{4 \times (3\times 10^{-2})^3}{3\times (1\times 10^{-3})^2} \\ \\ \\ \implies l = \frac{4 \times 27 \times 10^{-6}}{3 \times 10^{-6}} \\ \\ \\ \implies \boxed{l=36\, \, m}$


Thus, length of wire is 36 metres, which is Option C.




Hope it helps
Purva
Brainly Community