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

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

from wikipedia