Question

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.

± 0.24π

± 0.024π

± 0.06π

± 0.0004166

Answer 1

uhh

Answer 2

0.01/12 = relative error

Answer 3

A=pi*r^2

Answer 4

hmm

Answer 5

I used the formula for the area of a circle
A=pi*r^2
dA=2pi*r

to get the linear approx. at x=12

A=f(12)+f'(12)(x-12)
=144pi+24pi(x-12)
24pi(x-6) skipped some simplifying steps

Answer 6

I put the answers up

Answer 7

I keep getting 0.0164493

Answer 8

Oh wait nvm! @dan815 I got it

Answer 9

You find the area of the puddle for 12 inches then you pick either 12.01 or 11.99 as another radius and subtract 12^2*pi from it and you get +/- 0.24pi

Answer 10

12=144pi
12.01=12.01^2*pi

12.01^2*pi-144pi=0.24pi

Answer 11

ok

Answer 12

(0.01/12)*2*144pi=0.24 pi