The circumference of the equator of a sphere was measured to be 82 82 cm with a possible error of 0.5 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area to 4 decimal places.

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 square centimeters, of a sphere are represented by following formulas:

(1)

(2)

Where is the radius of the sphere, in centimeters.

By applying (2) in (1), we derive this expression:

(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:

(4)

Where:

- Measure circumference, in centimeters.

- Possible error in circumference, in centimeters.

If we know that and , then the maximum error is:

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

-6 is the correct option from the above given options

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step-by-step explanation: