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Question

The radius of a sphere is (6.3±0.1) cm. The percentage error in its volume is

A
0.16.3×100
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B
3×0.16.3×100
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C
0.1×1003.53
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D
3+(0.15.3×100)
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Solution

The correct option is B 3×0.16.3×100
Fractional error in radius is given by drr
Given,
Measurement of Radius of the sphere r±dr=6.3±0.1 cm
From this,
dr=0.1 cm, r=6.3 cm
We know that, Volume of sphere V=43π r3
Applying logarithm on both sides we get,
lnV=ln(4π3)+lnr3
Differentiating on both sides we get,
dVV=3×drr
% error in volume will be,
dVV×100=3×drr×100
% error in volume =3×0.16.3×100
Thus, option (b) is the correct answer.

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