Error in radius is 3%, what is error in volume of spher
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So, a 3 % error range [−0.03r,0.03r] , in r would be propagated in V(r) as;
V(r±0.03r)=43π(r±0.03r)3
and the relative error interval (range) of V(r) would be;
V(r±0.03r)−V(r)V(r)=[−0.081327,0.092727]
The calculation given by relative rates of change would give;
dV(r)V(r)=3drr
So, the relative rate of change of V would be three times that of r . However, these are NOT errors propagated. They are relative rates of change.
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