Miscellaneous Problems In Maths

Every answer needs to have steps. 

1. There is a cubic box of size 1m by 1m by 1m. It is filled to its capacity with solid spherical marbles, all of the same size. Then the box is filled with water. What should be the radius of the marble so that max water can be filled. And what is the minimum volume of water than can be filled? 
2. There is a circular park which has a path on the outside. What should be the ratio of the inner radius of the park to the width of the path so that the area of the path and that of the park are the same?

Additional reading

1. http://vbala99.blogspot.com/2015/06/maths-and-logic-puzzles.html
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