Question

The length of a wire is 4cm+_ 0.04cm, radius is 1cm +_ 0.01 cm . Find the volume

Answer 1

Answer:

Volume of the wire is $\rm 12.57\ cm^3\pm 0.38\ cm^3.$

Explanation:

Given:

• Length of the wire, $L\pm \Delta L = 4\ cm \pm 0.04\ cm$.

• Radius of the wire, $r\pm \Delta r = 1\ cm \pm 0.01\ cm$.

The wire is in cylindrical shape, therefore its volume is given by

$V=\pi r^2 L=\pi \times(1)^2\times (4) =12.57\ \rm cm^3.$

The uncertainty in the volume is given by

$\Delta V = \dfrac{2\Delta r}{r}+\dfrac{\Delta L}{L}$

The uncertainties in length and radius are given as

$\Delta L = 0.04\ cm\\\Delta r = 0.01\ cm$

Using these values,

$\dfrac{\Delta V}{V} = \dfrac{2\times 0.01}{1}+\dfrac{0.04}{4}=0.03\\\Delta V = 0.03\times V = 0.03\times 12.57=0.38\ \rm cm^3.$

Thus, the volume of the wire is given by

$V\pm \Delta V = \rm 12.57\ cm^3\pm 0.38\ cm^3.$

Answer 2

Answer:

12.57cm3+-0.38cm3

Explanation:

v=2πrl

v=2×22/7×(1×1)×4

v=12.57