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.

Question

Philoid · Accepted Answer

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

Now, it is given that r = 9m and Δr = 0.03m

We know that surface area of sphere (S) =

Now,

= (8πr)Δr

= 8π (9)(0.03)m²

= 2.16π m³

Therefore, the approximate error in calculating its surface area is 2.16π m³.