The approximate change in the total surface area of a right circular cone when the radius ‘r’ remains constant while altitude h changes by ‘ $α$ ’ is

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$\frac{πrhα}{\sqrt{r^{2} + h^{2}}}$

$\frac{πrh}{\sqrt{r^{2} - h^{2}}}$

$\frac{πhα}{\sqrt{r^{2} + h^{2}}}$

$\frac{πrhα}{\sqrt{r^{2} - h^{2}}}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} δh & = & α l^{2} = r^{2} + h^{2} \\ s & = & πrl + {πr}^{2} = πr \sqrt{r^{2} + h^{2}} \\ δs & = & \frac{πr}{2 \sqrt{r^{2} + h^{2}}} 2 hδh = \frac{πrhα}{\sqrt{r^{2} + h^{2}}} \end{array}$

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