Question

18. The Tennis for Champs company is looking into new ways to package tennis balls. The packaging engineer at the company is exploring options for vacuum packing the balls (removing the air from the containers in which they are packaged) so they will retain good bounce. He wonders how much air there is in a standard container of tennis balls. Find the amount of empty space in a cylindrical container that is 18 cm tall and contains three tennis balls 6 cm in diameter. Use 3.14 for pi.

Answer 1

Amount of empty space in the cylinder = 395.64 cm³

Explanation:

Since the cylinder contains 3 tennis balls each measuring 6 cm in diameter, we can say that the diameter of the cylinder is 6 cm because the balls are on top of each other. Since we have 18 cm is the height of the cylinder,then;

Formula for volume of a cylinder is;

V = πr²h

We are to use π = 3.14

Thus, V_cylinder = 3.14 × (6/2)² × 18

V_cylinder = 508.68 cm³

Volume of a tennis ball is;

V_tennis ball = (4/3)πr³

V_tennis ball = (4/3) × 3.14 × (6/2)³

V_tennis ball = 37.68 cm³

Thus, volume of 3 tennis balls = 3 × 37.68 = 113.04 cm³

Amount of empty space in the cylinder = V_cylinder - V_3 tennnis ball = 508.68 - 113.04 = 395.64 cm³