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Cone: Formulas of Surface Area and Volume

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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