If the radius of a cylinder is half the length of the edge

$$Radius\ of\ cylinder\ =\ \frac{1}{2}\cdot length\ of\ edge\ of\ a\ cube$$
$$Height\ of\ cylinder\ =length\ of\ edge\ of\ a\ cube$$
$$Ratio\ of\ volume\ of\ cube\ and\ cylinder=??$$
$$Volume\ of\ cube=\left(length\ of\ cube\right)^3=a^3$$
$$Volume\ of\ cylinder=\pi r^2h$$
$$r=a\cdot\frac{1}{2}=\frac{a}{2}\ and\ h=a$$
$$Volume\ of\ cylinder=\pi\cdot\left(\frac{a}{2}\right)^2\cdot a$$
$$Volume\ of\ cylinder=\pi\cdot\frac{a^3}{4}\ where\ a^3=volume\ of\ cube$$
$$=\frac{\pi}{4}\cdot volume\ of\ cube$$
$$The\ ratio\ of\ volume\ of\ cube\ to\ volume\ of\ cylinder=\frac{4}{\pi}$$

Hence, the correct answer is C