The radius of a puddle is claimed to be 12.0 inches, correct to within 0.01 inch. Use linear approximation to estimate the resul

Question

2 years ago

15

ting error, measured in square inches, in the area of the puddle.

2 answers:

navik [9.2K] · Answer 1 · 2022-07-06T09:12:40+03:00

8 0

Answer:

I think the answer is 23

Ahat [919] · Answer 2 · 2022-07-06T10:24:57+03:00

Answer:

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