A toy baseball bat comes with 3 plastic balls. The balls are in a box that is a rectangular solid. The box is just big enough to hold the 3 balls. The radius of the balls is 1.4 in. each What is the volume of the air in the box surrounding the balls?

31.4 in³

Step-by-step explanation:

The box is just big enough to hold the 3 balls, so it must have a length 6 times the radius of each ball, a width 2 times the radius, and a height 2 times the radius.

The volume of the box is:

V = (6r)(2r)(2r)

V = 24r³

The volume of the 3 balls is:

V = 3 (4/3 π r³)

V = 4πr³

So the volume of the air is:

V = 24r³ − 4πr³

V = (24 − 4π) r³

Since r = 1.4 inches:

V = (24 − 4π) (1.4 in)³

V ≈ 31.4 in³

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step-by-step explanation:

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