Personally, I wouldn't use differentiation to answer this question. If, in the 'worst case' scenario we over measure the outer measure and and length by the maximum possible error, and under measure (because we will be subtracting it) the inner radius, we would get outer radius of 10+ 1= 11 cm, length of 20+ 2= 22 cm and inner radius 8- .5= 7.5 cm we would get a volume of cubic centimeters. That is 4475- 2262= 2213 cubic centimeter larger than the "actual value".

If we under measure the outer radius and lengthby the maximum possible error, and over measure the inner radius, we would have outer radius 10-1= 9 cm, length 20- 2= 18 cm, and inner radius 8+ .5= 8.5 and get a volume of [tex] \pi(9^2- 8.5^2)(18)= 495 cubic centimeters That is 2262- 495= 1767 cubic centimeters less than the "actual value'.

The larger or fthose "errors" is 2213 cubic centimeters.