Question

The error in the measurement of radius of a sphere is 0.4% .Find the permissible error in the surface area ?

Answer 1

area is proportional to r².
and since the error is less than 5%. we can use approximation.
so % error in area= 2x% error in radius
. =2x0.4 %
. =0.8%

Answer 2

Given,

Error in the measurement of radius = 0.4%

To find,

Permissible Error in the surface area

Solution,

We know that,

The percentage error in measurement of the radius is given by

     Δr/r × 100 = 0.4%

Thus,

     Δr/r  =  0.4/100

The surface area of a sphere is given by,

     $S = 4\pi r^{2}$

Take ln and differentiate, we get,

     ΔS/S = 2(Δr/r)

              = 2 × 0.004

              = 0.008

The Permissible Error is given by

= (ΔS/S) × 100

= 0.008 × 100

= 0.8%

The Permissible Error in the surface area of a sphere is 0.8%.