The error is actually pessimistic. If you're an I.B. or A-level student, you could just say that the fractional or relative error on the volume is three times the fractional error on the radius, which does indeed give 170cm^3.[1] Doing it properly, one "sums the fractional errors in quadrature". -Square the fractional error on r, multiply by three and root the result to get the fractional error in volume. -That gives on 98cm^3.

[1] Can haz JS math filter?

For an American example of this see this sports blog relating to baseball pitches

http://worldsworstsportsblog.com/tag/margin-of-error/

Also of note is that roller hockey pitches have a 10% margin of error in terms of their size.
Finally, and closer to home, look at the recent case of Ian Bell given not out even though hawk eye said he was, as the ball was pitched outside of the 2.5m zone. This means the margin of error was deemed to high so couldn't be used accurately.

http://uk.eurosport.yahoo.com/02032011/28/icc-bats-its-2-5-metre-rule.html

The error is actually pessimistic. If you're an I.B. or A-level student, you could just say that the fractional or relative error on the volume is three times the fractional error on the radius, which does indeed give 170cm^3.[1] Doing it properly, one "sums the fractional errors in quadrature". -Square the fractional error on r, multiply by three and root the result to get the fractional error in volume. -That gives an error of 98cm^3.

[1] Can haz JS math filter?