The measurement of the radius of the end of a log is found to be 9 inches, with a possible error of 1/2 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.

Step-by-step explanation:

We are given that

Radius of end of a log, r= 9 in

Error, in

We have to find the error in computing the area of the end of the log by using differential.

Area of end of the log, A=

Now,

Approximate error in area

Using the values

Hence, the possible propagated error in computing the area of the end of the log

Step-by-step explanation:

radius, r = 9 inches

error = 0.5 inch

The area of the end is

A = 3.14 x r x r = 3.14 x 9 x 9 = 254.34 in^2

So, the area is given by

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