A drinking glass is in the shape of a frustum of a cone of height 14 cm.

We have,

Height of the frustum, $h=14 \mathrm{~cm}$,

Base radii, $R=\frac{16}{2}=8 \mathrm{~cm}$ and $r=\frac{12}{2}=6 \mathrm{~cm}$

The capacity of the glass = Volume of the frustum

$=\frac{1}{3} \pi h\left(R^{2}+r^{2}+r R\right)$

$=\frac{1}{3} \times \frac{22}{7} \times 14 \times\left(8^{2}+6^{2}+8 \times 6\right)$

$=\frac{1}{3} \times 22 \times 2 \times(64+36+48)$

$=\frac{44}{3} \times 148$

$=\frac{6512}{3} \mathrm{~cm}^{3}$

$\approx 2170.67 \mathrm{~cm}^{3}$

So, the capacity of the glass is 2170.67 cm3.