# A Laboratory Exercise in

Indirect Measurement

### Teacher Information

Here students are to indirectly measure something (the radius of a circle) that they are probably used to measuring directly with a ruler. They are given the sheet with a set of identical circles, a marble and a sheet of carbon paper. By covering the sheet with a random set of dots and finding the ratio of hits inside the circles to marbles thrown, an accurate and suprisingly precise value for the radius of one of the circles can be found. Students could then measure the circles and compare this answer with the answer found directly.

An interesting alternative, if the students are not allowed to ever measure the circles with a ruler, is to have them discuss among groups who has the best results and why. This activity is a nice analog to Rutherford's experiment where he found the size of gold nuclei (circles) by firing alpha particles (marbles) at a thin gold sheet (sheet of paper). Discuss with the students how Rutherford would have confirmed his results. He could not use a ruler to measure directly. He had to rely on the reproducibility of his results by other scientists. A student laboratory information sheet and a master page of circles are available.

This activity takes about one 55-minute period to complete.