My meeting can wait a moment. To work out the volume of a cylinder we need the square of the radius, not the diameter. Since 22/7 is accurate to only two decimal places as an approximation of pi, there's no point in taking any of the other figures to more than two places either:

Peter's formula (with the assumption regarding units as above) thus becomes:

.89 / (22/7 * 14.2^2)

= .89 / (633.73)

= .0014 ... (or, to two significant places, zero!)

Back to our units again: is there any way that this result can be out by three places, giving a value of 1.4mm, or is the logic amiss in the first place?

I always found it was best to return to SI units (kg for mass and metres cubed for volume) for doing these and this was my result

Density of gold (provided) 19320 kg/m3

Density of Silver (provided) 10490 kg/m3

Proportion of Gold (provided) 0.917

Prportion of silver (provided) 0.083

Density of coin 18587.11 kg/m3 (sum of densities * proportions)

Mass of coin (provided) 0.01598 kg

Volume of coin 8.59736E-07 m3 (mass/density)

radius of coin (provided) 0.0142 m

face area of coin 0.000633726 m2 volume/pi r squared

height of coin 0.001356637 m volume/face area

thickness of coin 1.356636746 mm