Can you please explain to me how to answer this question perfectly?  This is O level physics of year 2014, paper 4(Practical to Alternative) Thank you! 

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The student has two options; they can either infer the diameter based on mathematical calculations, or they can measure the diameter directly. 

I would perform both measurements, starting with the mathematical one, and then measuring the beaker as a means of checking if my mathematical prediction was correct.

Note that we don't have enough information on the beaker to determine its actual dimensions; volume for a cylinder is given by `pi*r^2*h`  , and we lack the values of both r and h. We are also being asked to find the outside diameter, and since the volume is a measurement of the inside of the beaker and doesn't include the thickness of the glass, we can't really use volume for any of the diameter measurements.

The diameter is simply the distance across a circle that passes through the center; or, the widest measurement. It is also twice the radius. We have two options; measure it directly with one of the rulers (the 30cm ruler would probably suffice) or measure the circumference of the beaker, deducing the diameter by using the circumference equation  equation.

1. Mathematical prediction:

  • Use the 2m thin string and mark a point near one of the ends with the marker. Wrap the string around the beaker until it overlaps itself (i.e. has been wrapped around the beaker once) and mark the overlap point with the marker. Then measure the distance between the two marked points on one of the rulers (30cm first, then half-meter if 30cm is too short). Do this three times to get a more accurate reading. 
  • Using the measurement of circumference, set this measurement equal to  and solve for r by dividing the measurement by `2pi`
  • Double the result to find the diameter.

An alternative to measuring with string might work if the marker is sufficiently wet: mark the outside of the beaker with a thin line of very wet marker, then roll the beaker across the lined paper, and measure the distance between the two marks left on the paper. 

2. Direct measurement

  • Using whichever ruler is most appropriate for the size of the beaker, attempt to measure the diameter directly. This can also be done by putting the beaker on the lined paper, tracing its contour with the pencil, and then measuring the drawing.

If the results do not sufficiently match, repeat both procedures.

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