Water is run at a constant rate of 1 ft^3/min to fill a cylindrical tank of radius 3ft and height 5ft. Assuming that the tank is initially empty, make a conjecture about the average weight of the water in the tank over the time period required to fill it, and then check your conjecture by integrating. (Take the weight density of water to be 62.4 lb/ft^3).

i found the volume of the cylinder to be 235.619 ft^3 which means it will take 235.619 min to fill the tank. so i set up the integral as (1/235.619) integral from (0 to 235.619) of (62.4) dt. i didn't get the correct answer. the correct answer is 1404(pi). please help me set up the correct integral.