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Kaylis [27]
4 years ago
12

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

Mathematics
1 answer:
Tcecarenko [31]4 years ago
5 0

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

__

(b) The relative error is ...

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

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