Bring in a nicely wound cord or garden hose (see below)
Explain to your students that you want them to determine the length of the cord or garden hose with the only condition being that they cannot stretch it out; they must find another way to measure the length.
Notice that the wound cord or garden hose is simply a bunch of circles stacked on top of one another. What if we calculated the circumference of the top circle and multiplied it by how many circles are formed by the winding process? Certainly you will be dealing with a margin of error here but it will at least get you in the ball park.
Note: be careful not to count a circle more than one time.