To calculate the tip, we need to find 35% of the dinner cost of $56.25.
First, we convert the percentage to a decimal: \[ 35% = 0.35 \]
Next, we multiply the dinner cost by the decimal: \[ \text{Tip} = 0.35 \times 56.25 \]
Now, let's calculate it: \[ \text{Tip} = 0.35 \times 56.25 = 19.6875 \]
Finally, we round this amount to the nearest hundredth (cent): \[ 19.6875 \approx 19.69 \]
Thus, Rafael should give a tip of $19.69.