Question

The volume V of the cylinder is given by the expression
V = πR2L .
The volume and length of the cylinder are measured as
V = 15.0 ± 0.5 cm3
L = 20.0 ± 0.1 cm.
Calculate the radius of the cylinder, with its uncertainty.

How do you find the UNCERTAINTY?

Answer 1

And the R is squared.

Answer 2

@Mashy @Abhisar @aaronq

Answer 3

First find the radius cuz you need it

\(V=\pi r^2L\rightarrow r=\sqrt{\dfrac{V}{\pi L}}=0.489~cm\)

then when you multiply or divide you have to use this formula to find the uncertainty:

\(\large \dfrac{\Delta x}{x}=\sqrt{(\dfrac{\Delta y}{y})^2+(\dfrac{\Delta z}{z})^2}\)

So for your problem it looks like this:

\(\large \dfrac{\Delta r}{r}=\sqrt{(\dfrac{\Delta V}{V})^2+(\dfrac{\Delta L}{L})^2}\)

\(\large \dfrac{\Delta r}{0.489}=\sqrt{(\dfrac{0.5}{15.0})^2+(\dfrac{0.1}{20.0})^2}\)


\( \large \Delta r =0.017 \approx 0.02\)

Answer 4

Thanks a lot !!!!!