In order to find the volume of a square-based pyramid, we will use the formula:
\[ V = \frac{1}{3} \times (\text{base area}) \times (\text{height}) \]
First, we need to calculate the base area of the square at the bottom of the pyramid. The formula for the area of a square is:
\[ \text{Base area} = \text{side length}^2 \]
Since we have a side length of 17 inches, the base area would be:
\[ \text{Base area} = 17^2 = 289 \text{ square inches} \]
Next, we will use the height of the pyramid, which is 9 inches, to find the volume of the pyramid using the volume formula.
\[ V = \frac{1}{3} \times 289 \times 9 \]
So the volume of the pyramid is:
\[ V = \frac{1}{3} \times 289 \times 9 = 867 \text{ cubic inches} \]
Finally, we want to round this volume to the nearest tenth of a cubic inch. Since the volume is already a whole number, there are no additional digits beyond the decimal place to consider, and thus, it remains:
\[ V \approx 867.0 \text{ cubic inches} \]
In conclusion, the volume of the square-based pyramid with a base side length of 17 inches and a height of 9 inches is approximately 867.0 cubic inches when rounded to the nearest tenth.
