Question

Three tennis balls fit snugly into a cylindrical container. Each tennis ball has a diameter of 4.5cm. What is the volume of air inside the container? (Please solve)

Answer 1

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