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

It is given that the radius of sphere is 9 m and error is 0.03 m.

Surface area of any sphere having radius r is given by,

S=4π r 2

Approximate error in surface area is given by,

ΔS= dS dr Δr = d( 4π r 2 ) dr Δr =8πrΔr

By substituting the given values in the above equation, we get

ΔS=8×π×9×0.03 =2.16π  m 2

Thus, the approximate error in surface area calculation is 2.16π  m 2 .