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The race circuit

Suppose the width of the path is constant and is 10m.
What difference in length between the right side and the left side of the path ?
Solution

The paper tape

Wrap a tape around a wine cork, diameter 2cm, then add 1m more paper. Build a large circle with the tape and put the cork in center.
Between the cork and the tape, there is about 15cm.
But now we'll do the same with Earth. Wrap a very long paper tape around Earth (40000km), add 1m more, reshape the circle, put the Earth in the midle of the circle.
Could a mouse walk between the tape and the Earth ?
Solution

A hole in a sphere

We drilled a hole in a sphere. The length of the hole is 6cm.
What is the remaining volume ?
Solution

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