Tennis balls with a diameter of 6.6 cm are sold in cans of three. The can is a cylinder. What is the volume of the space NOT occupied by the tennis balls?
First, let's calculate the total volume occupied by the three tennis balls.
Each tennis ball has a diameter of 6.6 cm, so the radius of each tennis ball is 6.6 cm / 2 = 3.3 cm.
The volume of each tennis ball can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3
V = (4/3) * π * (3.3)^3
V = 179.594 cm^3 (approximately)
The total volume occupied by the three tennis balls is 3 * 179.594 cm^3 = 538.782 cm^3.
Now, let's calculate the volume of the cylinder that contains the three tennis balls.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the cylinder and h is the height of the cylinder.
The radius of the cylinder is the same as the radius of the tennis balls, 3.3 cm.
Now, we need to find the height of the cylinder. Each tennis ball has a diameter of 6.6 cm, so when three tennis balls are stacked in the cylinder, the height of the cylinder is also 6.6 cm.
Therefore, the volume of the cylinder is:
V = π * (3.3)^2 * 6.6
V = 227.891 cm^3 (approximately)
Finally, the volume of the space NOT occupied by the tennis balls is the volume of the cylinder minus the total volume occupied by the tennis balls:
Volume not occupied = 227.891 cm^3 - 538.782 cm^3 = 311.891 cm^3
Therefore, the volume of the space not occupied by the tennis balls is 311.891 cm^3.