A Stick and A Ball

Geometry Level 4

On a bright and sunny day, I took a stick (of negligible width) and a ball to an empty, perfectly flat field. I held the stick perpendicular on the field and found that its shadow was as long as the stick itself. If I placed the ball down on the field and measured its shadow, starting from the point it touches the ground, it would be \(k\) times as long as the radius of the ball. Which of the following numbers is closest to the value of \(k\)?

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