If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

Let r be the radius of the sphere and Δr be the error in measuring the radius.

Now, it is given that r = 7m and Δr = 0.02m


We know that volume of sphere (V) =


Now,



= (4πr2)Δr


= 4π (72)(0.02)m3


= 3.92π m3


Therefore, the approximate error in calculating its volume is 3.92π m3.


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