Question

Error in the measurement of radius of sphere is 1% . Then the error in the measurement of volume is ?

Answer 1

For a sphere, the volume V=(4/3)πr^3
Taking log, we get logV=3logr+log(4/3)π
Differentiating both sides, we get
dV/V=3(dr/r)
Since error in the measurement of radius of sphere is 1%, dr/r=0.01=1%,
then dV/V is 0.03 or 3%
Hence the error in the measurement of volume is 3%