Question

The radius of a solid sphere is $24cm$. It is melted and drawn into a long wire of uniform cross section. Find the length of the wire if its radius is $1.2mm$.

• A. $12.8km$
• B. $128km$
• C. $1.8km$
• D. None of these

Answer 1

The correct option is A $12.8km$

We have,

$r_s=24cm$

We know that the volume of the sphere

$V_s=\frac{4}{3}\pi r_s^3$

So,

$V_s=\frac{4}{3}\pi (24{)}^3$

Let the length of the wire be $h$.

$r_l=1.2mm=0.12cm$

Since, the wire is like as cylinder.

So, the volume of wire

$=\pi r^{2}h$

Since, the sphere is melted and drawn make a wire.

So,

$\pi (0.12{)}^{2}h=\frac{4}{3}\pi (24{)}^3$

$h=\frac{\mathrm{4.8.24.24}}{\left(0.12\right).\left(0.12\right)}$

$h=\frac{\mathrm{4.8.24.24}}{\frac{12}{100}.\frac{12}{100}}$

$h=4\times 8\times 200\times 200$

$h=1280000cm$

$h=12800m$

$h=12.8km$

Hence, this is the answer.