Question

Kent needs to know the volume of a sphere. When he measures the radius, he gets 135.4 m with an uncertainty of +4.6 cm. What's the uncertainty of the volume?

Answer 1

Answer:

The uncertainty in the volume of the sphere is $1.059\times 10^{4} m^{3}$

Solution:

As per the question:

Measured radius of the sphere, R = 135.4 m

Uncertainty in the radius, $\Delta R = 4.6 cm = 4.6\times 10^{- 2} = 0.046 m$

We know the volume of the sphere is:

$V_{s} = \frac{4}{3}\pi R^{3}$

We know that the fractional error for the given sphere is given by:

$\frac{\Delta V_{s}}{V_{s}} = \frac{4}{3}\pi.\frac{|Delta R}{R}$

where

$\Delta V_{s}$ = uncertainty in volume of sphere

Now,

$\Delta V_{s} = \frac{4}{3}\pi 3R^{2}\Delta R$

Now, substituting  the suitable values:

$\Delta V_{s} = 4\pi (135.4)^{2}\times 0.046 = 1.059\times 10^{4} m^{3}$