The volume inside the can that is not taken up by the three tennis balls is 21.21 in³.
Volume of the cylindrical can
Since the tennis balls have a radius r = 1.5 in which touch the sides of the cylindrical can, the radius of the cylindrical can equals the radius of the tennis ball.
Also, since the balls touch each other and the top and bottom of the cylindrical can, we have that the height of the cylindrical can,
h = 3d where
- d = diameter of tennis ball = 2r where
- r = radius of tennis ball.
So, h = 3d
= 3(2r)
h = 6r
So, the volume of the cylindrical can V = πr²h
= πr² × 6r
= 6πr³
Volume occupied by the tennis balls
Since each tennis ball is a sphere of radius r, its volume is V' = 4πr³/3.
Since there are 3 tennis balls, the total volume of tennis balls is V" = 3V'
= 4πr³/3 × 3
= 4πr³
Volume inside can not taken up by the three tennis balls.
So, the volume inside the can not taken up by the 3 tennis balls is V₀ = V - V"
= 6πr³ - 4πr³
V₀ = 2πr³
Since r = 1.5 in,
V = 2πr³
V = 2π(1.5 in)³
V = 2π(3.375 in³)
V = 6.75π in³
V = 21.21 in³
So, the volume inside the can that is not taken up by the three tennis balls is 21.21 in³.
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