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Q.

Error in the measurement of volume of a sphere is 3%. Then error in the measurement of its surface area is

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a

1.5 %

b

3 %

c

2 %

d

2.5 %

answer is D.

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Detailed Solution

$\begin{array}{l} \frac{4}{3} π r^{3} = V \Rightarrow r = {(\frac{3 V}{4 π})}^{1 / 3} \\ ∴ S = 4 π r^{2} = 4 π {(\frac{3}{4 π})}^{2 / 3} . V^{\frac{2}{3}} = k . v^{\frac{2}{3}} \\ ∴ (\frac{Δ S}{S}) = \frac{2}{3} (\frac{Δ V}{V}) = \frac{2}{3} \times 3 % = 2 % \end{array}$

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