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, we need to calculate the volume of each tennis ball.
The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter of the tennis ball is 6.6 cm, the radius is half of that, which is 3.3 cm.
Plugging this into the formula, we get V = (4/3)π(3.3)^3 ≈ 150.05 cm^3.
Since there are three tennis balls in the can, the total volume occupied by the tennis balls is 3 * 150.05 = 450.15 cm^3.
Now, we need to find the volume of the cylinder can. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is the height.
Since the diameter of the tennis balls is 6.6 cm, the radius of the cylinder is half of that, which is 3.3 cm. Assuming the height of the can is also 6.6 cm (to accommodate the tennis balls), the volume of the cylinder is V = π(3.3)^2 * 6.6 ≈ 231.44 cm^3.
The space not occupied by the tennis balls in the can is the volume of the cylinder minus the volume of the tennis balls, so this is 231.44 - 450.15 = -218.71 cm^3.
Since the volume cannot be negative, it means that the volume of the space not occupied by the tennis balls is zero.