A wire of diameter 10 mm is drawn by melting the sphere of radius 9 cm . The length of wire would be

Correct option is D

​Given:

Diameter of wire = 10 mm = 1 cm

Radius of wire = 0.5 cm

Radius of sphere = 9 cm

Concept Used:

When a sphere is melted and reshaped into a wire, volume remains constant.

Formula Used:

Volume of sphere:

$$V_{\text{sphere}} = \frac{4}{3} \pi r^3$$​​

Volume of wire (cylinder):

$$V_{\text{wire}} = \pi r^2 h$$​​

h = length of the wire

Solution:

Volume of sphere = Volume of wire 

​$$\frac{4}{3} \pi (9)^3 = \pi \times \left(\frac{1}{2}\right)^2 \times h \\ \ \\ \frac{4}{3} \times 729 = \frac14 \times h \\ \ \\ \implies h = \frac{4 \times 4 \times 729}{3} \\ \ \\ h = 3888\ cm = 38.88 \ m$$​​