How much water in cubic centimeters is needed to fill a cylindrical tube with three tennis balls (radius 3 cm) inside?

To determine how much water is needed to fill a cylindrical tube with three tennis balls inside, we first need to calculate the total volume of the water that would fill the tube, taking into account the volume occupied by the tennis balls.

The formula for the volume of a sphere is given by ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere. For each tennis ball with a radius of 3 cm, we can calculate the volume of one ball:

[

V_{ball} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36\pi

]

Since there are three tennis balls, the total volume occupied by the balls is:

[

V_{total_balls} = 3 \times 36\pi = 108\pi

]

Next, we need to find the volume of the cylindrical tube. To fill the tube, we add the volume of water that would equate to the volume the three balls occupy, but we need to subtract the volume of the balls from the total volume of the cylinder.

The question assumes the cylindrical