Question

If the volume of a right circular cone is V, the area of it's curved surface is S, radius of the base is r, height is h and semi-vertical angle is α, then show that:-

$\\ \sf{\rightarrow{S = \dfrac{\pi {h}^{2} \tan(\alpha) }{ \cos( \alpha )}} = \dfrac{\pi {r}^{2} }{ \sin( \alpha ) } \: square \: units}$
$\\ \sf{ \rightarrow{V = \dfrac{1}{3} \pi {h}^{3} { \tan }^{2} \alpha = \frac{\pi {r}^{3} }{3 \tan( \alpha ) }} \: cube \: units}$

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Answer 1

Answer:

If the volume of a right circular cone is V, the area of it's curved surface is S, radius of the base is r, height is h and semi-vertical angle is α, then show that:-

$\\ \sf{\rightarrow{S = \dfrac{\pi {h}^{2} \tan(\alpha) }{ \cos( \alpha )}} = \dfrac{\pi {r}^{2} }{ \sin( \alpha ) } \: square \: units}$

$\\ \sf{ \rightarrow{V = \dfrac{1}{3} \pi {h}^{3} { \tan }^{2} \alpha = \frac{\pi {r}^{3} }{3 \tan( \alpha ) }} \: cube \: units}$

● Kindly don't spam!

● Quality answer needed!

Answer 2

Step-by-step explanation:

Answer in the figure

Hope this will help you