If the error in the measurement of radius of a sphere is $2\%$ then the error in the determination of volume of the sphere will be ........ $\%$
A $2$
B$4 $
C$6$
D$8$
AIPMT 2008, Easy
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C$6$
c Percentage error in radius is given as $2 \%$
$\frac{\Delta r }{ r } \times 100=2 \%$
Volume of sphere $V =\frac{4 \pi}{3} r ^{3}$
$\frac{\Delta V }{ V } \times 100=3 \times \frac{\Delta r }{ r } \times 100=3 \times 2=6 \%$
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