(3) If a regular quadrilateral pyramid with a base edge length of 2 has an inscribed sphere with a radius of $\frac{1}{2}$, then the volume of this regular quadrilateral pyramid is $\qquad$ .
(3) $\frac{16}{9}$ Hint: Let $\theta$ be the dihedral angle between the base and a side face of the square pyramid, then
$$
\tan \frac{\theta}{2}=\frac{\frac{1}{2}}{1}=\frac{1}{2},
$$

thus
$$
\tan \theta=\frac{2 \tan \frac{\theta}{2}}{1-\tan ^{2} \frac{\theta}{2}}=\frac{4}{3} .
$$

Therefore, the height of the pyramid is $1 \times \tan \theta=\frac{4}{3}$. So the volume is
$$
\frac{1}{3} \times 2^{2} \times \frac{4}{3}=\frac{16}{9} \text {. }
$$