You need to evaluate the surface area of the sphere such that:

`A= 4*pi*r^2` , where r is the radius of sphere

You should use the formula of circumference to write the radius in terms of circumference of circle such that:

`C = 2pi*r =gt r = C/(2pi)`

You should substitute `C/(2pi)` for r in equation of surface area such that:

`A = 4*pi*C^2/(4pi^2)`

`A = C^2/pi`

You should differentiate both sides such that:

`dA = 2C/pi (dc)`

You should substitute 82.000 for C and 0.5 cm for dc such that:

`dA = (2*82.000/3.14)*0.5`

`dA = 26101.410`

**Hence, using linear approximation yields `dA = 26101.410` .**

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