Question

What is the relative uncertainty of an area of a circle (in percentage, one significant digit) if the diameter is measured to be 4.0 cm and the uncertainty in the diameter measurement is 0.1 cm?

Answer 1

For calculating approximate uncertainty we proceed as follows:

We know that Area A=(π×D²)/4

If we take ln of both sides we will get

lnA = ln(π/4) + 2lnD

Now just take differentials

ΔA/A = 2*ΔD/D

Here, ΔA/A = Relative uncertainty of an area of a circle

ΔD = 0.1

D = 4.0

Substituting these value in above equation, we get

Relative uncertainty of an area of a circle (in %) = (2*0.1/4)*100

Relative uncertainty of an area of a circle = 5.0%