Question

The radius of the base of a right circular cone of semi-vertical angle α is r. Show that its volume is $\frac{1}{3}{\mathrm{\pi r}}^3$ cot α and curved surface area is πr² cosec α.

Answer 1

$$\begin{gathered} \sin \alpha =\frac{r}{l} \\ \Rightarrow r\cos ec\alpha =l \\ \tan \alpha =\frac{r}{h} \\ \Rightarrow rcot\alpha =h \end{gathered}$$

= πr² cosec α.