Final answer:
The total volume of the space inside the cylinder that is unoccupied is 134.408 cubic inches.
Step-by-step explanation:
The first step is to calculate the volume of the cylinder using the formula V = πr²h, where r is the radius and h is the height. In this case, the radius is 4 inches and the height is 8 inches, so the volume of the cylinder is V = 3.142 × (4 inches)² × 8 inches = 402.496 cubic inches.
The next step is to calculate the volume of the basketball. A sphere's volume is given by the formula V = (4/3)πr³, where r is the radius. Since the radius of the basketball is also 4 inches, the volume of the basketball is V = (4/3) × 3.142 × (4 inches)³ = 268.088 cubic inches.
To find the volume of the space inside the cylinder that is unoccupied by the basketball, we subtract the volume of the basketball from the volume of the cylinder. Therefore, the total volume of the space inside the cylinder that is unoccupied is 402.496 cubic inches - 268.088 cubic inches = 134.408 cubic inches.