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Q.

The volume of a sphere is calculated by the formula $V = \frac{4}{3} {πr}^{3} .$ If $δr$ is the error in measuring the radius r, then the approximate error in the volume is

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a

$4 πr {δr}^{2}$

b

$2 πr {δr}^{2}$

c

$4 π {δr}^{2}$

d

$4 {πr}^{2} δr$

answer is D.

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Detailed Solution

$v = \frac{4}{3} {πr}^{3} \Rightarrow δv = \frac{4}{3} π 3 r^{2} δr = 4 π r^{2} δr$

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