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

The uncertainty in the volume of the sphere is
`1.059* 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* 10^(- 2) = 0.046 m`

We know the volume of the sphere is:

`V_(s) = (4)/(3)\pi R^(3)`

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

`(\Delta V_(s))/(V_(s)) = (4)/(3)\pi.(|Delta R)/(R)`

where

`\Delta V_(s)` = uncertainty in volume of sphere

Now,

`\Delta V_(s) = (4)/(3)\pi 3R^(2)\Delta R`

Now, substituting the suitable values:

`\Delta V_(s) = 4\pi (135.4)^(2)* 0.046 = 1.059* 10^(4) m^(3)`