A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 in length of uniform thickness. The diameter of the wire is

Given,

\( \Large r_{1} \) = 1 cm, \( \Large h_{1} \) = 30 cm, \( \Large h_{2} \) = 300 cm

Volume of rod = Volume of wire

=> \( \Large \pi r_{1}^{2}h_{1} = \pi r_{2}^{2}h_{2} \)

=> \( \Large \pi \times \left(1\right)^{2} \times 30 = \pi \times r_{2}^{2} \times 300 \)

=> \( \Large r_{2}^{2} = \frac{30}{300} \)

Therefore, \( \Large r_{2} = \frac{1}{\sqrt{10}}cm \)

Therefore, diameter = 2\( \Large r_{2} \)

\( \Large \frac{2}{\sqrt{10}} cm \)