Question

The dimension of a rectangular shape is 5.9 by 4.1mm s measured with a veneer calliper whose minimum scale is 0.05 mm. The percentage error in its surface area is approximately.

Answer 1

e% = 2.2%

Step-by-step explanation:

In the measurements it is very important the precision of the readings and the knowledge of how the uncertainty or errors in each measurement propagates when carrying out the different calculations

In this case the area of ​​the body is its length l = 5.9 mm, for its width a = 4.1 mm

S = l a

The error can be calculated using derivatives and considered the worst of all cases

Δs = ds /dl Δl + dS /da Δa

in this case the derivatives are very simple

dS / dl = a

dS / Da = l

we substitute

ΔS = a Δl + l Δa

this is the absolute error

Let's calculate its value

Δs = 4.1 0.05 + 5.1 0.05

Δs = 0.5 mm²

the percentage error is this error between the magnitude of the mediated by 100

e% = ΔS / S 100

e% = 0.5 / (5.1 4.1) 100

e% = 2.2%