A tank in the shape of a hemisphere has a diameter of 24 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?

Step 1 ：Given that the diameter of the tank is 24 feet, we can calculate the radius as \( r = \frac{d}{2} = \frac{24}{2} = 12 \) feet.

Step 2 ：The volume \( V \) of a hemisphere is given by the formula \( V = \frac{2}{3} \pi r^3 \). Substituting \( r = 12 \) feet into the volume formula gives \( V = \frac{2}{3} \pi (12)^3 = \frac{2}{3} \pi 1728 = 3628.8 \) cubic feet.

Step 3 ：The weight \( W \) of the liquid in the tank is given by the formula \( W = \rho V \), where \( \rho \) is the density of the liquid. Given that the density of the liquid is 92.5 pounds per cubic foot, substituting \( \rho = 92.5 \) pounds per cubic foot and \( V = 3628.8 \) cubic feet into the weight formula gives \( W = 92.5 \times 3628.8 = 335,664 \) pounds.

Step 4 ：Rounding to the nearest full pound gives a total weight of \( \boxed{335,664} \) pounds.