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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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$\frac{π r h α}{\sqrt{r^{2} + h^{2}}}$

$\frac{π r h}{\sqrt{r^{2} - h^{2}}}$

$\frac{π r h α}{\sqrt{r^{2} - h^{2}}}$

$\frac{π h α}{\sqrt{r^{2} + h^{2}}}$

answer is A.

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Detailed Solution

$δ h = α, T = π r l + π r^{2}; T = π r (\sqrt{r^{2} + h^{2}} + π r^{2})$

$\Rightarrow f (h) = \sqrt{2} π h^{2} ∴ A.value = f (h) + f^{'} (h) \times Δ h$

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