$$V = \pi r^2 h$$
where V represents the volume, r represents the radius, and h represents the height of the tank.
Given that the diameter is 16 ft, the radius can be calculated as half of the diameter, which is 8 ft. And the height is given as 2 ft.
Substituting these values into the formula, we get:
$$V = \pi (8^2) (2)$$
$$V = \pi (64) (2)$$
$$V = 128\pi$$
Now, to convert cubic feet to gallons, we need to multiply the volume in cubic feet by the conversion factor 7.48 gallons per cubic foot.
$$V_{gallons} = V_{cubicfeet} \times 7.48$$
Substituting the value of V in cubic feet, we get:
$$V_{gallons} = 128\pi \times 7.48$$
$$V_{gallons} \approx 2988.48 \text{ gallons}$$
Therefore, the cylindrical tank with a diameter of 16 ft and a depth of 2 ft can hold approximately 2988.48 gallons.