Question

A metallic cube of edge $1cm$ is drawn into a wire of diameter $4mm$, then the length of the wire is:

• A. $\frac{10}{\pi }cm$
• B. $10\pi cm$
• C. $\frac{25}{\pi }cm$
• D. $1000cm$

Answer 1

Answer: (C)

$\frac{25}{\pi }cm$

Edge of cube $=1$ cm

Volume of cube ${\left(1\right)}^3=1c{m}^3=1000m{m}^3$

Diameter of wire $=4mm$

Radius of wire $=2mm$

Now, volume remains same

Therefore, volume of wire $=$ volume of cube

$\pi r^{2}h=1000m{m}^3\pi \times 2\times 2\times h=1000h=\frac{1000}{4\pi }=\frac{250}{\pi }mmh=\frac{25}{\pi }cm$