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The percentage error in the measurement ...

The percentage error in the measurement of the radius of a sphere is 1.5%. What would be the percentage error in the volume of the sphere ?

Text Solution

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Let the radius of the sphere = `rpmDeltar`
Then according to the question, `(Deltar)/rxx100=1.5%`
or `(Deltar)/r=.015`
Volume of the sphere is `V=4/3pir^(3)`
As per the rule for combination of error for exponents
`(DeltaV)/V=3(Deltar)/r`
= `3xx0.015`
`(DeltaV)/V=0.045`
Percentage error `(DeltaV)/V=100=0.045xx100=4.5%`
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