If side of a cube is 10 cm and error in it is 0.05 cm then match the following and choose correct answer.
List-I List-II
I. Error in surace area of cube A) 15
II. Percentage error in surface area B) 6
III. Error in volume C) 1.5
IV. Percentage error in volume D) 0.05
E) 1

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I II III IV

B D E A

I II III IV

A C B E

I II III IV

B E A C

I II III IV

A C E D

answer is D.

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Detailed Solution

$x = 10 σx = 0.05 I) S = 6 x^{2} \Rightarrow σs = 12 x σx = 120 \times 0.05 = 6 II) \log S = \log 6 + 2 \log x \frac{1}{S} σs = \frac{2}{x} σx \Rightarrow \frac{σs}{s} \times 100 = 2 \times \frac{0.05}{10} \times 100 III) v = x^{3} \Rightarrow σr = 3 x^{2} σx = 300 \times 0.05 = 15 IV) \log v = 3 \log x \Rightarrow \frac{σr}{r} \times 100 = 3 \frac{σx}{x} \times 100 = \frac{3 \times 0.05 \times 100}{10} = 1.5$