What is the area and uncertainty in area of one side of a rectangular plastic brick that has a length of (21.4 ± 0.3) cm and a width of (9.8 ± 0.1) cm? (a 210 cm2 (b) what if? if the thickness of the brick is (1.2 t0.3) cm, what is the volume of the brick and the uncertainty in this volume? (give your answers in cm.) 021.73 x 421.30 x )cm3

a) A = (209.7 ± 5.0) cm^2

b) V = (251.6 ± 75.5) cm^3

Explanation:

The area will be simply

21.4 * 9.8 = 209.7 cm^2

For multiplication of uncertainties you have to first convert them to relative uncertainties

Then we add those together and this is the relative uncertainty of the product

(209.7 ± 2.4%) cm^2

And we can convert it to absolute uncertainty:

Then the area is expressed as:

A = (209.7 ± 5.0) cm^2

For volume

209.7 * 1.2 = 251.6 cm^3

And the relative uncertainty is

So the volume with relative uncertainty is:

(251.6 ± 30%) cm^3

And converting it to absolute uncertainty:

V = (251.6 ± 75.5) cm^3

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explanation: