Question

If the error in the measurement of radius of a
sphere is 2%, then the error in the determina-
tion of volume of the sphere will be
(a) 4%
(b) 6%
(c) 8%
(d) 2%​

Answer 1

${\mathcal{\red{ANSWER}}}$

$\sf{Correct\;answer\;is\;(b)\;6\%.}$

${\mathcal{\red{EXPLANATION}}}$

Given:

$\tt{\dfrac{\Delta r}{r} \times 100 = 2\%}$

$\sf{We\;know,}$

$\bf{Volume\;of\;sphere = \dfrac{4}{3} \pi r^{3}}$

Then,

$\tt{\implies \dfrac{\Delta v}{v} \times 100 = \pm 3 \bigg(\dfrac{\Delta r}{r} \times 100\bigg)}$

$\tt{\implies \pm 3 \times 2 = \pm 6\%}$

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