Snail's Pace

Stage: 3 Short Challenge Level: Challenge Level:1

A snail is at one corner of the top face of a cube with side length $1$m. The snail can crawl at a speed of $1$m per hour. What proportion of the cube's surface is made up of points which the snail could reach within one hour?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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