The volume of the larger hemisphere is $\frac{2}{3}\pi(1^3)=\frac{2}{3}\pi$.
Since the volume of each smaller hemisphere is equal, the volume of each smaller hemisphere is $\frac{2}{3\cdot 27} \pi=\frac{2}{81}\pi$.
The volume of a hemisphere is $\frac{1}{2}\cdot \frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3$.
Setting the volume of each smaller hemisphere equal to this expression, we have $\frac{2}{3}\pi r^3=\frac{2}{81}\pi$.
Simplifying, we find $r^3=\frac{1}{81}$, so $r=\boxed{\frac{1}{3}}$.
The answer is: \frac{1}{3}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
After filling a hemisphere-shaped bowl with a radius of 1 foot with chocolate, the chocolate is evenly distributed among 27 congruent, smaller hemisphere-shaped molds. What is the radius of each of the smaller molds, in feet?

### Answer:
