Tennis balls are packaged into cylindrical cans to ship and sell. Three tennis balls fit into one cylinder so that the height of the three b

Question

Tennis balls are packaged into cylindrical cans to ship and sell. Three tennis balls fit into one cylinder so that the height of the three balls is equal to the height of the cylinder. and the diameter of one ball is equal to the diameter of the cylinder. The radius of one tennis ball is 1.3 inches. How much air space is in the cylinder around the tennis balls?

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Jasmine 5 days 2021-10-12T10:37:18+00:00 1 Answer 0

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    2021-10-12T10:38:58+00:00

    Answer:

      about 13.8 in³

    Step-by-step explanation:

    The volume of air is the difference between the volume of the cylinder of radius 1.3 inches and height 7.8 inches, and that of three spheres, each with a radius of 1.3 inches.

    The formula for the volume of a cylinder is …

      V = πr²h

    The formula for the volume of a sphere is …

      V = (4/3)πr³

    For h = 6r, the difference is …

      (cylinder volume) – 3×(sphere volume) = πr²·(6r) – 3×(4/3)πr³

      = πr³(6 -4)

      = 2πr³ = 2π(1.3 in)³ = 4.394π in³

      ≈ 13.8 in³ . . . . air space in the cylinder of tennis balls

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