Question

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

Answer 1

Let * be the surface area, r be the radius of the sphere.

Given, r = 9 cm

Then, dr = Approximate error in radius r and dS = Approximate error in surface area

Now, we know that surface area of sphere is given by

• = 4πr2

On differentiating both sides w.r.t. r,we get

Hence, approximate error in surface area is 2.16π cm2/cm.