Question

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 in surface area.

Answer 1

Let r be the radius of the sphere and ∆ r be the error in measuring the radius.
Then,
r = 9 m and ∆ r = 0.03 m
Now, the surface area of the sphere (S) is given by,

Hence, the approximate error in calculating the surface area is 2.16π m².