Answer:
We can use the formula for the volume of a cylinder to find the volume of the barrel:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
First, we need to find the radius of the barrel. The diameter is given as 23.25 inches, so the radius is half of that:
r = 23.25 / 2 = 11.625 inches
Next, we can substitute the given values into the formula:
V = π(11.625)^2(34.9)
V ≈ 14,898.65 cubic inches
Rounding this to the nearest hundredth, we get:
V ≈ 14,898.65 cubic inches ≈ 14,898.64 cubic inches (rounded to the nearest hundredth)
Therefore, the volume of the barrel is approximately 14,898.64 cubic inches.