Answer:
Volume of air inside the cylinder = 71.6 cm³
Step-by-step explanation:
Step 1: Determine height and radius of the cylinder
Since the three tennis balls fits in closely into the cylindrical container, the height of the cylinder is equal to the sum ofnthe diameters of the three balls.
Also, the radius of the cylinder is equal to the radius of the tennis balls.
Height of cylinder = 3 × 4.5 cm = 13.5 cm
Radius of cylinder/balls = diameter of ball / 2 = 4.5 cm / 2 = 2.25 cm
Step 2: Determination of the volume of the cylinder
Volume of a cylinder = πr²h
π = 22/7; r = 2.25 cm; h = 13.5 cm
Volume of cylinder = 22/7 × (2.25 cm)² × 13.5 cm
Volume of cylinder = 214.8 cm³
Step 3: Determining the volume of the three balls
Volume of a sphere = 4πr³/3
Volume of three balls = 4πr³/3 × 3 = 4πr³
Volume of the three balls = 4 × 22/7 × (2.25 cm)³ = 143.2 cm³
Step 4: Determining the volume of air
Volume of air inside the cylinder = Volume of cylinder - volume of the three balls
Volume of air = 214.8 cm³ - 143.2 cm³ = 71.6 cm³
Therefore, volume of air inside the cylinder = 71.6 cm³
