Question

A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?

Answer 1

calculate the volume of both and then make them equal... to get the length =9cm

Answer 2

Answer: The length of the wire is 9 cm.

Step-by-step explanation:

Since we have given that

Radius of a metallic sphere = 12 cm

So, Volume of sphere is given by

$=\frac{4}{3}\pi r^3\\\\=\frac{4}{3}\times \frac{22}{7}\times 12\times 12\times 12$

Since the metallic sphere is melted and drawn into a wire whose radius of cross section = 16 cm

Since wire is in the shape of cylinder.

So, volume of cylinder is given by

$\pi r^2h\\\\=\frac{22}{7}\times 16\times 16\times h$

As we know that

Volume of sphere = Volume of wire

$\frac{4}{3}\frac{22}{7}\times 12\times 12\times 12=\frac{22}{7}\times 16\times 16\times h\\\\h=\frac{4\times 12\times 12\times 12}{16\times 16\times 3}\\\\h=9\ cm$

Hence, the length of the wire is 9 cm.