If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.

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Text solutionVerified

Solution: r=9

δ r

=0.03
we know,

v = \frac{4}{3} π r^{3}

differentiate with respec to r

\frac{δ v}{δ r} = \frac{δ}{δ r} (\frac{4}{3} π r^{3})

δ v = 4 π r^{2} δ r

δ v = 4 (3.14) (9^{2}) (0.03)

δ v = 30.520 c m^{3}

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Question Text	If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.
Answer Type	Text solution:1
Upvotes	150