Final answer:
The volume of the cylindrical barrel of oil is found using the formula V = πr²h. By converting the diameter to radius, and using the given height, the volume is calculated as approximately 14825.97 cubic inches.
Step-by-step explanation:
To find the volume of a cylindrical barrel of oil in cubic inches, we start by using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.
First, we need to convert the diameter to radius by dividing by two. The radius of the barrel is 23.25 inches / 2 = 11.625 inches. We are given the height of the barrel as 34.9 inches.
Using these values, we calculate the volume:
V = π × (11.625 inches)² × 34.9 inches
V = 3.14159 × (11.625 inches)² × 34.9 inches
V = 3.14159 × 135.390625 inches² × 34.9 inches
V = 3.14159 × 4725.06514 cubic inches
V = 14825.97 cubic inches (rounded to the nearest hundredth)
Therefore, the volume of the oil barrel is approximately 14825.97 cubic inches.