A solid brass sphere of radius 15 cm is drawn into a wire of diameter 6 mm. The length (in cm) of the wire is:

Let's assume the radius of the sphere and wire(cylinder) are $$R_s$$ and $$R_c$$ respectively.

A solid brass sphere of radius 15 cm is drawn into a wire of diameter 6 mm.

$$R_s$$ = 15 cm

$$R_c = \frac{6}{2} = 3mm$$

As we know that 10mm = 1cm.

1mm = 0.1cm

$$R_c = 3mm = 0.3cm$$

Let's assume the length of the wire is $$l$$ cm.

volume of sphere = volume of wire(cylinder)

$$\frac{4}{3}\times\pi\ \times\left(R_s\right)^3=\pi\ \times\left(R_c\right)^2\times\ l$$

$$\frac{4}{3} \times(15)^3 = (0.3)^2 \times l$$

$$\frac{4}{3}\times3375=0.09l$$

$$4\times1125=0.09l$$

$$4\times12500=l$$

$$l = 50000$$ cm