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If there is an error 0.01 cm in the measurement of the radius 10 cm of a cylinder of fixed height 20 cm then percentage error in the volume is

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0.0002

0.02

0.2

0.002

answer is A.

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Detailed Solution

$h = 20 r = 10 δr = 0.01 v = π r^{2} h \log v = \log π + 2 \log r + \log h \frac{1}{v} δv = 0 + \frac{2}{r} δr + 0 \frac{dv}{v} \times 100 = \frac{2}{10} \times 0.01 \times 100 = \frac{1}{5}$

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