Physical World Units And Measurements Ques 42
42. 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:
[2008]
(a) $4 \%$
(b) $6 \%$
(c) $8 \%$
(d) $2 \%$
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Answer:
Correct Answer: 42.(b)
Solution:
- (b) Given, error in the measurement of radius
of a sphere $\frac{\Delta r}{r} \times 100=2 \%$
Volume of the sphere $V=\frac{4}{3} \pi r^{3}$
$\therefore$ Error in the volume $\frac{\Delta V}{V} \times 100$
$= \pm 3 \cdot \frac{\Delta r}{r} \times 100=3 \times 2 \%= \pm 6 \%$
BETA
