The international unit of measurement for diamonds is carats. As we all know, the value of a diamond is directly proportional to the square of its weight (carat). A 3-carat diamond is worth $54,000.

(1) Write the functional relationship of v;

(2) If a diamond is cut into two diamonds with the weight ratio of 1∶3, find the percentage of value loss;

(3) The mathematical knowledge you have learned proves that when a diamond is cut into two pieces, the percentage of value loss is the largest when it is cut according to the weight ratio of1:1.

(Percentage of value loss =; Weight loss in cutting is not included)