The volume \( V \) of a pyramid can be expressed by the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Given that the volume varies jointly with the base area and height, we can also write:
\[ V = k \times \text{Base Area} \times \text{Height} \]
where \( k \) is a constant.
We know that the volume of one pyramid is 24 cubic inches when the base area is 3 square inches and the height is 24 inches. From this information, we can calculate the constant \( k \):
\[ 24 = k \times 3 \times 24 \]
Solving for \( k \):
\[ 24 = 72k \] \[ k = \frac{24}{72} = \frac{1}{3} \]
Now, we can use this value of \( k \) to find the volume of the pyramid with a base area of 10 square inches and a height of 9 inches.
Using the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
Substituting the values:
\[ V = \frac{1}{3} \times 10 \times 9 \] \[ V = \frac{1}{3} \times 90 \] \[ V = 30 \]
Thus, the volume of the pyramid is \( \boxed{30} \) cubic inches.