The diameter of a metallic solid sphere is 42 cm. It is melted and drawn into a wire with a cross-sectional diameter of 0.6 cm. Find the length (in metre) of the wire.​

Correct option is A

Given:

The diameter of the metallic solid sphere is 42 cm.

The cross-sectional diameter of the wire is 0.6 cm.

We need to find the length of the wire.

Formula Used:

Volume of sphere = $$\frac{4}{3} \pi R^3$$

Volume of wire (cylinder) = $$\pi r^2 h$$​​

Solution:

Radius of sphere(R) = $$\frac{42}{2} = 21 \, \text{cm}$$  

Radius of wire(r) = $$\frac{0.6}{2} = 0.3 \, \text{cm}$$​​

Volume of Sphere = Volume of wire(cylinder) 

​$$\frac{4}{3}\times \pi \times(21)^3 = \pi \times (0.3)^2 \times h \\ \ \\ \frac{4}{3}\times (21)^3 = (0.3)^2 h \\ \ \\ \implies h = \frac{4\times 21\times 21\times 21}{3\times 0.3 \times 0.3} = 137200 \, \text{cm}$$​​

Thus, the length of the wire is 1372 meters.