Final answer:
The volume of the empty space inside the cylindrical tube can be found by calculating the volume of the cylinder and the volume of the tennis balls, and then subtracting the volume of the tennis balls from the volume of the cylinder. The volume of the cylinder can be calculated using the formula V = πr²h, and the volume of the tennis balls can be calculated using the formula V = (4/3)πr³. By plugging in the appropriate values, we can find that the volume of empty space inside the tube is approximately -16.522 cubic inches.
Step-by-step explanation:
To find the volume of empty space inside the cylindrical tube, we need to determine the volume of the cylinder and the volume of the tennis balls.
The volume of a cylinder can be calculated using the formula: V = πr²h, where r is the radius and h is the height of the cylinder. The radius is half the diameter, so r = 2.6 inches / 2 = 1.3 inches. The height is the same as the diameter of the tennis ball, which is 2.6 inches. Plugging these values into the formula, we get: V_cylinder = π(1.3 inches)²(2.6 inches) = 10.628 cubic inches.
The volume of a tennis ball can be calculated using the formula: V = (4/3)πr³, where r is the radius of the tennis ball. The radius is half the diameter, so r = 2.6 inches / 2 = 1.3 inches. Plugging this value into the formula, we get: V_tennis_ball = (4/3)π(1.3 inches)³ ≈ 9.05 cubic inches.
Since each tube holds 3 tennis balls, the total volume of the tennis balls is: 3 tennis balls x 9.05 cubic inches/tennis ball = 27.15 cubic inches.
The volume of empty space inside the tube is the difference between the volume of the cylinder and the total volume of the tennis balls: V_empty_space = V_cylinder - V_tennis_balls = 10.628 cubic inches - 27.15 cubic inches ≈ -16.522 cubic inches.
Therefore, the volume of empty space inside the tube is approximately -16.522 cubic inches.