The volume \( V \) of a rectangular pyramid can be calculated using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given:
- Volume \( V = 22,750 , \text{cm}^3 \)
- One dimension of the base \( b_1 = 30 , \text{cm} \)
- Height (altitude) \( h = 65 , \text{cm} \)
The formula for the base area \( A \) of the rectangular base is:
\[ A = b_1 \times b_2 \]
where \( b_2 \) is the other dimension of the base.
We can substitute the variables into the volume formula:
\[ 22,750 = \frac{1}{3} \times (30 \times b_2) \times 65 \]
First, simplify the right side:
\[ 22,750 = \frac{1}{3} \times 30 \times 65 \times b_2 \]
Calculating \( \frac{1}{3} \times 30 \times 65 \):
\[ 30 \times 65 = 1950 \]
\[ \frac{1}{3} \times 1950 = 650 \]
Now the equation becomes:
\[ 22,750 = 650 \times b_2 \]
To find \( b_2 \):
\[ b_2 = \frac{22,750}{650} \]
Calculating this gives:
\[ b_2 = 35 \]
Thus, the other dimension of the pyramid's base is:
\[ \boxed{35 , \text{cm}} \]