The problem states that the snow on Cherry Street is melting, which corresponds to a decrease in snow levels, so we use a negative value for the rate of melting.

The melting rate is:

$\dfrac{1}{3} \text{ cm per hour}.$

To find the total change in the snow depth after 3 hours, we multiply the melting rate by the number of hours:

$\text{Total change} = - \left( \dfrac{1}{3} \times 3 \right) = -1 \text{ cm}.$

Therefore, the total change in depth of the snow after 3 hours is a decrease of:

$\boxed{-1 \text{ cm}}.$

Would you like a more detailed explanation? Or do you have any other questions?

Here are 5 related questions to deepen your understanding:

1. What would be the total change if the snow melted for 5 hours at the same rate?
2. How would the problem change if the snow increased instead of melting?
3. If the snow melted at a rate of $\dfrac{1}{2} \text{ cm per hour}$, what would be the total change after 3 hours?
4. What if the snow melted for only 2 hours at the same rate of $\dfrac{1}{3} \text{ cm per hour}$?
5. If the snow started increasing instead at a rate of $\dfrac{1}{3} \text{ cm per hour}$, what would be the total increase after 3 hours?

Tip: When dealing with negative values in real-world scenarios (such as melting or decreases), always check the context to ensure you assign the correct sign to the change.