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If the radius of a sphere is measured as 10cm with an error of 0.01 cm, then find the approximate error in calculating its volume.

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a

0.4π cm3

b

0.41π cm3

c

0.42π cm3

d

4π cm3

answer is D.

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Detailed Solution

measuring the radius, then r=10cm and Δr=0.01cm. Now the volume V of the sphere is given byV=43πr3dVdr=4πr2dV=dVdrΔr=4πr2Δr=4π(10)2(0.01)cm3=4πcm3Thus, the approximate error in calculating the volume is 4π cm3

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