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in Surface Areas And Volumes by (49.2k points)
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If S denotes the area of the curved surface of a right circular cone of height h end semi-vertical angle a, then S equals

(a) πh2 tan2α 

(b) \(\frac13\) πh2 tan2α 

(c) πh2 sec α tan α 

(d) \(\frac13\) πh2 sec α tan α

1 Answer

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Best answer

(c) πh2 sec α tan α

S = πrl, where r = radius, l = slant height, h = height

Now \(\frac{r}{h}\) = tan α ⇒ r = h tan α

l = \(\sqrt{h^2+r^2}\)

\(\sqrt{h^2+r^2\,tan^2\,α}\)

\(\sqrt{h^2(1+tan^2\,α)}\)

\(\sqrt{h^2\,sec^2\,α}\) = h sec α

∴ S = π. h tan α. h sec α = πh2 sec α tan α.

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