**Toolbox:**

- Let $y=f(x)$
- $\Delta x$ denote a small increment in $x$
- $\Delta y=f(x+\Delta x)-f(x)$
- $dy=\big(\large\frac{dy}{dx}\big)\ $$\Delta x$
- Surface area=S=$4\pi r^2$

Step 1:

Radius of the sphere =$70$ cm

Error in measurement =$\Delta r = 0.03$ cm

Surface area=S=$4\pi r^2$

$\Rightarrow \large\frac{dS}{dr}$$=8\pi r$ [Differentiating with respect to r]

Step 2:

$\Delta S=\large\frac{ds}{dr}$$\times \Delta r$

$\quad\;\;=8\pi r\times 0.03$

$\quad\;\;=8\pi \times 70 \times 0.03$

$\quad\;\;= 52.8\; cm^2$