To find the unit cost per pizza, we need to divide the total cost by the number of pizzas purchased.
The total cost of the order is $58.50, and he bought 6 pizzas.
The calculation is:
\[ \text{Unit cost per pizza} = \frac{\text{Total cost}}{\text{Number of pizzas}} = \frac{58.50}{6} \]
Calculating that gives:
\[ \text{Unit cost per pizza} = 9.75 \]
Thus, the unit cost per pizza is $9.75.
The correct answer is C. $9.75.