Percent Uncertainty in Spherical Beach Ball Volume

In summary, the percent uncertainty in the volume of a spherical beach ball with a radius of 0.84 +/- 0.06m is approximately 0.86%. This was calculated by using the power law for uncertainty and multiplying the result by 100.
  • #1
George3
31
0

Homework Statement



What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 0.84 + or - 0.06m?
Answer must have 2 sig figs.

Homework Equations


The Attempt at a Solution


I found the volume of the sphere with .84 radius which would be 3.0 m^3 and then I don't know what to do next.
 
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  • #2
If y is related to x by a power law,

y = axn, then the fractional uncertainty is

[tex]\frac{\Delta y}{y}=n\frac{\Delta x}{x}[/tex]
 
  • #3
Consider what happens to the uncertainty in a variable when you cube the variable (should be a standard treatment in the manipulation of uncertainties in variables)
 
  • #4
Fightfish said:
Consider what happens to the uncertainty in a variable when you cube the variable (should be a standard treatment in the manipulation of uncertainties in variables)
So are you saying I should cube the .06 and then divide that by the 3.0m^3?
 
  • #5
Could you show your equations and attempts, please?
 
  • #6
(.84)^3(pi)(4/3) = 2.5 m^3

.06^3 = 2.2x10^-4

2.2x10^-4 / 2.5 = 8.6x10^5

(8.6x10^5) x 100% = .0086%
 
  • #7
Not how it works. Here, n = 3. Therefore, the fractional uncertainty is

[tex]\frac{\Delta V}{V} = 3\times\frac{0.06}{0.84}[/tex]

Multiply by 100 and you have percent uncertainty.
 

1. What is percent uncertainty?

Percent uncertainty is a measure of the amount of uncertainty or error associated with a measurement or calculation. It is expressed as a percentage and helps to indicate the reliability or accuracy of a result.

2. How is percent uncertainty calculated?

Percent uncertainty is calculated by dividing the absolute uncertainty of a measurement or calculation by the measured value, and then multiplying by 100%. The absolute uncertainty is determined by taking the average of the maximum and minimum possible values for the measurement.

3. Why is percent uncertainty important?

Percent uncertainty is important because it provides a way to evaluate the reliability of a measurement or calculation. It allows scientists to assess the level of uncertainty or error present in their results, which is crucial for drawing accurate conclusions and making informed decisions.

4. How does percent uncertainty affect the validity of results?

A higher percent uncertainty indicates a greater level of error or uncertainty in the results. This can affect the validity of the results, as a higher uncertainty means there is a greater chance of the results being incorrect. Therefore, it is important to keep percent uncertainty as low as possible to ensure the validity of the results.

5. Can percent uncertainty be reduced?

Yes, percent uncertainty can be reduced by improving the precision and accuracy of the measurements or calculations. This can be done by using more precise instruments, increasing the number of measurements taken, or using more advanced mathematical techniques. However, it is impossible to completely eliminate percent uncertainty as there is always some level of error or uncertainty in scientific measurements and calculations.

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