Matilda has a 100 g rock sample. she knows that the rock contains uranium-238 and that the half-life of uranium-238 is 4.5 × 109 years. if she cuts the rock sample in half, what happens to the half-life of the uranium?

The half life is not related with the size of the sample but it is an intensive property of the material, in this case uranium-238.

Cutting the sample in half does not change the properties of uranium-238, so both halves will have the same kind of uranium and so the half-life of uranium-238 remains the same, i.e. 4.5 - 10^9 years.