To evaluate the formula \( v = \frac{bh}{3} \) with \( B = 9 \) in² and \( h = 32 \) in, substitute the values into the formula.
\[ v = \frac{9 , \text{in}^2 \times 32 , \text{in}}{3} \]
Calculating the multiplication first:
\[ 9 \times 32 = 288 \]
Now, substitute that back into the formula:
\[ v = \frac{288 , \text{in}^3}{3} \]
Now, divide \( 288 \) by \( 3 \):
\[ v = 96 , \text{in}^3 \]
Thus, the evaluated volume \( v \) is
\[ \boxed{96 , \text{in}^3} \]