Phy 101
A rectangular plate has a length of (21.3 +/- .2 ) cm and a width of (9.8 +/- .1) cm. Calculate the aea of the plate, including the uncertainty.

Question

Phy 101
A rectangular plate has a length of (21.3 +/- .2 ) cm and a width of (9.8 +/- .1) cm. Calculate the aea of the plate, including the uncertainty.

aaronq · Answer

$A=l*w=21.3~cm*9.8 ~cm=208.74~cm^2$

$\dfrac{s_A}{A}=\sqrt{(\dfrac{s_l}{l})^2+(\dfrac{s_w}{w})^2}$

$\dfrac{s_A}{208.74~cm^2}=\sqrt{(\dfrac{0.2}{21.3})^2+(\dfrac{0.1}{9.8})^2}=2.894$

$s_A=2.894~cm^2$

lilsis76 · Answer

lol Hi @aaronq could you explain what the s^A means, and what you did to get the answer. I want to be sure to understand. THe book is confusing me

aaronq · Answer

$\huge s_x$ is the uncertainty in measurement x.

so $\huge s_A$ is the uncertainty in the area. Likewise, $\huge s_l$ and $\huge s_w$ are the uncertainties given for the length and the width, respectively. 

Looked where i subbed in the values, after that it's just algebra.

lilsis76 · Answer

oh...okay

aaronq · Answer

you know, i just noticed i wrote something incorrectly.

ignore the 2.984 in the third line, it shouldn't be there.

lilsis76 · Answer

okay, im still studying what you did exactly. let me see if I have it right.

lilsis76 · Answer

OKAY @aaronq  i got SA= 2.893
thank you so much. UGH! math haha

aaronq · Answer

awesome!