The radius of a puddle is claimed to be 12.0 inches, correct to within 0.01 inch. Use linear approximation to estimate the resulting error, measured in square inches, in the area of the puddle.

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Mathematics

1 September, 02:23

The radius of a puddle is claimed to be 12.0 inches, correct to within 0.01 inch. Use linear approximation to estimate the resulting error, measured in square inches, in the area of the puddle.

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Karlie Banks · Answer 1

Karlie Banks 1 September, 02:35

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I think the answer is 23

Case Page · Answer 2

the resulting error is about 0.754 in²

Step-by-step explanation:

A (r) - A (r0) ≈ dA/dr· (r - r0)

The area of a circle is given by ...

A (r) = πr²

so the derivative is

dA/dr = 2πr

and the area error is ...

dA/dr· (r - r0) = 2π (12 in) (0.01 in) = 0.24π in² ≈ 0.754 in²