To find the volume of a pyramid with a square base, we use the formula:
[tex]\[ \text{Volume} = \frac{1}{3} \times (\text{base area}) \times \text{height} \][/tex]
Since the base is a square, the base area is simply the side length squared:
[tex]\[ \text{Base area} = \text{side length} \times \text{side length} \][/tex]
Given that the side length of the base is [tex]\( 18.5 \)[/tex] inches, the base area is:
[tex]\[ \text{Base area} = 18.5 \times 18.5 \][/tex]
[tex]\[ \text{Base area} = 342.25 \text{ square inches} \][/tex]
Now, we can calculate the volume of the pyramid using the height [tex]\( h = 10.9 \)[/tex] inches:
[tex]\[ \text{Volume} = \frac{1}{3} \times 342.25 \times 10.9 \][/tex]
[tex]\[ \text{Volume} = \frac{1}{3} \times 3730.525 \][/tex]
[tex]\[ \text{Volume} = 1243.5083333333333 \text{ cubic inches} \][/tex]
Rounding this to the nearest tenth gives us:
[tex]\[ \text{Volume} \approx 1243.5 \text{ cubic inches} \][/tex]
So, the volume of the pyramid is approximately 1243.5 cubic inches.
