Question

The radius of a circular disk is given as 21 cm with a maximum error in measurement of 0.2 cm.

(a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2
(b) What is the relative error?

Answer 1

Answer:

  (a) 26.39 cm²

  (b) 1.9%

Step-by-step explanation:

(a) The area formula is ...

  A = πr²

so the derivative of the area is ...

  A' = 2πrr'

In terms of differentials, the area error is approximately ...

  ΔA = 2πr·Δr

Filling in the numbers, we have ...

  ΔA = 2π(21 cm)(0.2 cm) = 8.4π cm² ≈ 26.39 cm²

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(b) The relative error is ...

  e = ΔA/A = (2πr·Δr)/(πr²) = 2Δr/r = 2(.2)/21 ≈ 1.9%