The volume of a chemical solution in a tank is described by the formula \(\frac{kT^2c}{p}\), where k is a constant, T is the p temperature, c is the concentration of the chemical solution, and p is the atmospheric pressure. The solution in the tank can be either hot or cold. When hot, c is half of what it is when cold, p is double what it is when cold, and T is triple what it is when cold. If the tank can be no more than \(\frac{3}{4}\) full when hot for safety reasons, what is the maximum fraction of capacity to which 4 the tank can be filled when the solution is cold?