Cone
Height of a cone: It is the length of the line segment joining the vertex to the centre of the base; VO.
Slant height: It is the length of the line segment joining the vertex to any point on the circular part of the base; VA.
Radius of cone: It is the radius of base circle of cone; OA.
Following are formulas of cone
Relation between Slant height l, Height h and radius of right circular cone r
Since $\angle VOA=90{}^\circ ,$ by Pythagoras theorem
$V{{A}^{2}}=O{{A}^{2}}+V{{O}^{2}}$
${{l}^{2}}={{r}^{2}}+{{h}^{2}}$
$l=\sqrt{{{r}^{2}}+{{h}^{2}}}$
For a right circular cone of base radius r, slant height l, height h,
(i) Curved Surface Area of a cone = $\pi rl$ sq. unit
(ii) Total Surface Area of a cone = base area + Curved surface area
= $\pi {{r}^{2}}+\pi rl$
= $\pi r(r+l)$ sq. unit
(iii) Volume of a cone = (Area of base circle) x height
= $\frac{1}{3}\times \pi {{r}^{2}}\times h=\frac{1}{3}\pi {{r}^{2}}h$ cu. unit
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