# 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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