1. 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?
To find the volume of the space not occupied by the tennis balls, we first need to find the volume of the can and then subtract the volume of the three tennis balls.
Volume of the can:
The can is a cylinder, so we use the formula for the volume of a cylinder:
V_can = πr^2h
Where r is the radius of the can (half the diameter) and h is the height of the can.
Given that the diameter of the tennis ball is 6.6 cm, the radius is 6.6/2 = 3.3 cm.
Let's assume the height of the can is equal to the diameter of the tennis ball, so h = 6.6 cm.
Therefore,
V_can = π(3.3)^2(6.6)
V_can = π(10.89)(6.6)
V_can = 226.7 cm^3
Volume of three tennis balls:
The volume of one tennis ball can be calculated using the formula for the volume of a sphere:
V_ball = (4/3)πr^3
V_ball = (4/3)π(3.3)^3
V_ball = (4/3)π(35.937)
Since there are three tennis balls in the can, the total volume of all three would be:
V_total_balls = 3 * (4/3)π(35.937)
V_total_balls = 3 * 47.916 π
V_total_balls = 143.748 π cm^3
Now, to find the volume of the space not occupied by the tennis balls:
V_space = V_can - V_total_balls
V_space = 226.7 - 143.748 π
V_space ≈ 226.7 - 450.207
V_space ≈ 223.5 cm^3
Therefore, the volume of the space not occupied by the tennis balls is approximately 223.5 cm^3.