For this problem, we must first determine the shadow of the whole ball, and then find out its maximum size.

For a three-meter-high bamboo pole, the length of the shadow is the root number 3, so it can be seen that the angle between the sun and the ground is 60 degrees.

Considering that sunlight is a kind of parallel light, when sunlight strikes a ball at an angle of 60 degrees, the shadow of the ball is an ellipse, and its long axis is three times the square root of the ball diameter, so the longest shadow of a ball with a radius of one meter is three times the square root of three meters.