What is the formula to find the volume of the space inside a cylindrical container that is not occupied by three tennis balls?
The formula to find the volume of the space inside a cylindrical container that is not occupied by three tennis balls is to subtract the volume of all three balls from the volume of the cylinder. The formula for the volume of the cylinder is πR²h, where h = 6r and R = r. The formula for the volume of the ball is (4/3)πr³. By putting these values into the equations and calculating, we have:
Volume = π(r)²(6r) - 3((4/3)πr³)
Volume = 6πr³ - 4πr³
Volume = 2πr³
Therefore, the volume of the space inside the cylinder not occupied by the balls is 2πr³.
Understanding the Calculation
Volume of Cylinder:
The volume of a cylinder is calculated by multiplying the area of the base (πR²) by the height (h). In this case, the height of the cylinder is given as 6 times the radius of the ball, and the radius of the ball is represented as 'r'. Therefore, the formula becomes:
Volume of Cylinder = π(r)²(6r) = 6πr³
Volume of Balls:
Since there are three tennis balls in the cylinder, we need to calculate the total volume occupied by the balls. The formula for the volume of a ball is (4/3)πr³. By multiplying this by 3, we get:
3((4/3)πr³) = 4πr³
Subtracting Volume of Balls from Volume of Cylinder:
By subtracting the volume of the balls from the volume of the cylinder, we can find the volume of the space that is not occupied by the balls:
Volume = 6πr³ - 4πr³ = 2πr³
Therefore, the formula 2πr³ represents the volume of the space inside the cylinder that is not occupied by the three tennis balls.
About Tennis Balls
Unique Equipment for Tennis:
A tennis ball is a specialized piece of equipment designed specifically for the sport of tennis. Typically, a standard can of tennis balls contains three balls. This number allows players to have a spare ball for the first and second serves during gameplay.
Ball Specifications:
According to ITF (International Tennis Federation) rules, tennis balls must have a diameter between 2.5 and 2.7 inches. The size of the ball can have an impact on its responsiveness and control during play. In terms of weight, ITF regulations state that a tennis ball should weigh between 56 and 59.4 grams.
In conclusion, understanding the volume of the space inside a cylindrical container not occupied by tennis balls involves mathematical calculations based on the properties of the cylinder and the balls. Additionally, having knowledge of tennis ball specifications is crucial for players to adhere to regulations and optimize their performance on the court.