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Question

Length of a thin cylinder as measured by vernier callipers having least cound 0.01 cm is 3.25 cm and its radius of cross-section is measured by a screw gauge having least count 0.01 mm as 2.75 mm. The percentage error in the measurement of volume of the cylinder will be

A
2%
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B
3%
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C
1%
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D
1.5
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Solution

The correct option is B 3%
V=πr2hV=πd222h=πd2h4V=πd2h4

taking log; logy=logπ4+2logd+logh

differentiating; dvV=2d(d)d+dhh......(i) According to question, h=3.25 cmdh=0.01 cmr=2.75 mmdr=0.01 mm

from (i)dyV=2d(2r)r+dhhdyV=4drr+dhh=4(0.012.75+0.013.25)=0.03

% error in y=0.03×100%.=3%.

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