The measurement of the radius of the end of a log is found to be 14 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.
A) square inches
B) square inches
C) square inches
D) square inches
E) square inches

Question

The measurement of the radius of the end of a log is found to be 14 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.
A) square inches 
B) square inches 
C) square inches 
D) square inches 
E) square inches

Quizplus · Accepted Answer

- The formula for the area of a circle is A = πr^2
- Taking the derivative with respect to r, we get dA/dr = 2πr
- We can use differentials to estimate the change in area if the radius changes by Δr, which is approximately ΔA = (dA/dr)Δr
- In this case, the radius has a possible error of 0.11 inches, so Δr = 0.11 inches
- Plugging in r = 14 inches, we get dA/dr = 2π(14) = 28π
- Thus, ΔA = (28π)(0.11) ≈ 9.68 square inches
- The closest choice is C, which is 11ec1854_fdba_a5de_acfc_cbe1fb2e464d_TBX8702_11 square inches.

The Measurement of the Radius of the End of a Log