Answer:
The maximum error in the calculated surface area is approximately 8.3083 square centimeters.
Step-by-step explanation:
The circumference ( ), in centimeters, and the surface area (
), in centimeters, and the surface area ( ), in square centimeters, of a sphere are represented by following formulas:
), in square centimeters, of a sphere are represented by following formulas: 
 (1)
 (1)
 (2)
 (2)
Where  is the radius of the sphere, in centimeters.
 is the radius of the sphere, in centimeters.
By applying (2) in (1), we derive this expression:

 (3)
 (3)
By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area ( ), in square centimeters:
), in square centimeters:
 
 
 (4)
 (4)
Where:
 - Measure circumference, in centimeters.
 - Measure circumference, in centimeters.
 - Possible error in circumference, in centimeters.
 - Possible error in circumference, in centimeters.
If we know that  and
 and  , then the maximum error is:
, then the maximum error is:

The maximum error in the calculated surface area is approximately 8.3083 square centimeters.