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- 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 =$9m$

Error in measurement =$\Delta r$

$\qquad\qquad\qquad\quad\;\;=0.03m$

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

$S=4\pi r^2$

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

Step 2:

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

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

$\quad\;\;=8\pi \times 9\times 0.03$

$\quad\;\;=72\pi \times 0.03$

$\quad\;\;=2.16\pi m^2$

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