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

Explanation

Let r be the radius of the sphere and Δr be the error in measuring the radius.
Then,` r=9 m` and `Δr=0.03 m`
Now, the surface area of the sphere (S) is given by,
`S=4pi^2`


`implies frac{dS}{dr}=8pir^2`


`therefore dS=frac{dS}{dr}Δr`


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