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?

The uncertainty in the volume of the sphere is

Solution:

As per the question:

Measured radius of the sphere, R = 135.4 m

Uncertainty in the radius,

We know the volume of the sphere is:

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

where

= uncertainty in volume of sphere

Now,

Now, substituting  the suitable values:

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