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, S = 4πr2

$\frac{ds}{dr}$=8πr

ds=($\frac{ds}{dr}$)∇r

=(8πr)∇r

=8π(9)(0.03)m2

2.16πm2

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