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svetoff [14.1K]
3 years ago
15

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 t

he uncertainty of the volume?
Physics
1 answer:
kondor19780726 [428]3 years ago
5 0

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}

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