**Manhattan Prep**

The volume of a chemical solution in a tank is described by the formula \(\dfrac{kT^2c}{p},\) where k is a constant, T is the 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 if 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 3/4 full when hot for safety reasons, what is the maximum fraction of capacity of which the tank can be filled when the solution is cold?

A. 1/9

B. 1/6

C. 1/5

D. 1/3

E. 2/3

OA D