The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.

Question

The measurement of the radius of the end of a log is found to be 28 inches, with a possible error of  inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.

Quizplus · Accepted Answer

The formula for the area of a circle is A = πr^2. Taking the differential of this equation with respect to r, we have dA = 2πr dr.

Substituting the given values, we have r = 28 inches and dr = 0.11 inches.

Plugging these values into the differential equation, we have:

dA = 2π(28)(0.11)
dA ≈ 19.78 square inches

Therefore, the possible propagated error in computing the area of the end of the log is approximately 19.78 square inches or 11eaa595_658f_6d39_a696_933dc78f902f_TB4584_11_TB4584_11.

The correct answer is C.

The Measurement of the Radius of the End of a Log