Choose the correct answer of the following question:

We have,

Radius of the solid sphere, $R=9 \mathrm{~cm}$ and

Radius of the solid cylinder, $r=9 \mathrm{~cm}$

Let the height of the cylinder be $h$.

Now,

Volume of the cylinder $=$ Volume of the sphere

$\Rightarrow \pi r^{2} h=\frac{4}{3} \pi R^{3}$

$\Rightarrow h=\frac{4 R^{3}}{3 r^{2}}$

$\Rightarrow h=\frac{4 \times 9 \times 9 \times 9}{3 \times 9 \times 9}$

$\therefore h=12 \mathrm{~cm}$

Hence, the correct answer is option (a).