Work Shown:
[tex]\text{SA} = 2\pi*r^2 + 2\pi*r*h\\\\\text{SA} \approx 2*3.14*2^2 + 2*3.14*2*10\\\\\text{SA} \approx 150.72\\\\[/tex]
She'll need approximately 150.72 square inches of wrapping paper.
Note: The circular base is 4 inches across, which is the diameter. Cut this in half to get r = d/2 = 4/2 = 2 inches for the radius.