The volume of a right circular cylinder with its height equal to the radius is

We have,

Height $=$ Base radius i. e. $h=r$

As,

Volume of the cylinder $=25 \frac{1}{7} \mathrm{~cm}^{3}$

$\Rightarrow \pi r^{2} h=\frac{176}{7}$

$\Rightarrow \frac{22}{7} \times h^{2} \times h=\frac{176}{7}$

$\Rightarrow h^{3}=\frac{176 \times 7}{7 \times 22}$

$\Rightarrow h^{3}=8$

$\Rightarrow h=\sqrt[3]{8}$

$\therefore h=2 \mathrm{~cm}$

So, the height of the cylinder is 2 cm.