Sizing a cube
[All measurements are in cm, or for volume, cubic cm.]
The edge of a cube is a number selected randomly in the range [1, 3].
This puts the volume in the range [1, 27]. What is the chance in per cent, to 2 decimal places, that the volume is in the lower half of that range (i.e., in the range [1, 14])?
The answer is 70.51.
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1 solution
For the volume to be 14 or less, the length of the edge has to be less than or equal to 2.41014.
So the allowed interval for the edge is [1, 2.41014], which is 1.41014 cm, dividing by 2 and converting to a percentage yields 70.507%, so to 2 decimal places that's 70.51%.