Question

A cylindrical gas bottle has a radius of 4.5 cm and a height of 30.0 cm. The uncertainty in both measurements is 0.1 cm. The directly calculated volume (V = π r2 h) of the bottle is 1908.5 cm3. Using the high/low method, which of the following is the best approximation to the uncertainty in this calculation?
4.5cm^3
0.1cm^3
30cm^3
90cm^3
0.0314cm^3

Answer 1

Answer:

The uncertainty in this calculation is 90 cm³

(d) is correct option.

Explanation:

Given that,

Radius of cylindrical bottle = 4.5 cm

Height = 30.0 cm

Uncertainty in both = 0.1 cm

Volume of bottle = 1908.5 cm³

We need to calculate the uncertainty in this calculation

Using formula of volume

$V=\pi r^2 h$

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

Put the value into the formula

$\dfrac{\Delta V}{1908.5}=\dfrac{0.2}{4.5}+\dfrac{0.1}{30}$

$\Delta V=1908.5\times(\dfrac{0.2}{4.5}+\dfrac{0.1}{30})$

$\Delta V=90\ cm^3$

Hence, The uncertainty in this calculation is 90 cm³