(i) Since the standard deviation is $0, all rides must cost the same, which is the mean of $2.50. Therefore, the roller coaster and the water slide each cost $2.50 per ride.

(ii) Let the cost of the revolving drum be $x. The equation for the mean cost is:

\(1 \times 2.5 + 3 \times 2.5 + 6 \times x = 3.76 \times 10\)

\(6x = 37.6 - 10\)

\(x = 4.6\)

\(The cost of the revolving drum is $4.60. Now, calculate the variance:\)

\(\sigma^2 = \frac{(2.5^2 \times 1 + 2.5^2 \times 3 + 4.6^2 \times 6)}{10} - 3.76^2\)

\(\sigma = 1.03\)