Smaller Random Squares

A factory manufactures wooden squares of 4 square centimeters. Due to some manufacturing defect, the side length of the square varies uniformly between $1\text{ cm}$ and $3\text{ cm}.$

Manager Bob wants to know how frequently the squares are smaller, i.e. less than $4\text{ cm}^2$ in area. He made the following observations:

1. The area of the square to be manufactured next is a random quantity between $1\text{ cm}^2$ and $9\text{ cm}^2.$
2. So, the probability that the area of the next square is less than $4\text{ cm}^2$ is $\frac{3}{8}.$

Is Bob correct?