The circumference of a sphere was measured to be
76

c
m
with a possible error of
0.5

c
m
.

(a) use differentials to estimate the maximum error in the calculated surface area. (round your answer to the nearest what is the relative error? (round your answer to three decimal

(b) use differentials to estimate the maximum error in the calculates volume. (round your answer to the nearest what is the relative error? (round your answer to three decimal

To solve this problem we will apply the concepts related to the calculation of the surface, volume and error through the differentiation of the formulas given for the calculation of these values in a circle. Our values given at the beginning are

The radius then would be

And

PART A ) For the Surface Area we have that,

Deriving we have that the change in the Area is equivalent to the maximum error, therefore

Maximum error:

The relative error is that between the value of the Area and the maximum error, therefore:

PART B) For the volume we repeat the same process but now with the formula for the calculation of the volume in a sphere, so

Therefore the Maximum Error would be,

Replacing the value for the radius

And the relative Error