To find the other dimension of the pyramid's base, we can use the formula for the volume of a rectangular pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
The base area of a rectangular pyramid can be calculated as:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
Here, the volume \( V \) is given as \( 22,750 , \text{cm}^3 \), the length is \( 30 , \text{cm} \), and the height is \( 65 , \text{cm} \).
First, substitute the known values into the volume formula:
\[ 22,750 = \frac{1}{3} \times (30 \times \text{Width}) \times 65 \]
Now, simplify the right-hand side:
\[ 22,750 = \frac{1}{3} \times 30 \times 65 \times \text{Width} \]
Calculating \( \frac{1}{3} \times 30 \times 65 \):
\[ \frac{1}{3} \times 1950 = 650 \quad (\text{since } 30 \times 65 = 1950) \]
Thus, the equation becomes:
\[ 22,750 = 650 \times \text{Width} \]
Now, solve for the Width:
\[ \text{Width} = \frac{22,750}{650} \]
Calculating this gives:
\[ \text{Width} = 35 \]
Therefore, the other dimension of the pyramid's base is:
\[ \boxed{35 , \text{cm}} \]