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Right circular cone[edit]
Volume[edit]
For a circular cone with radius r and height h, the base is a circle of area {\displaystyle \pi r^{2}}  and so the formula for volume becomes^[6]
{\displaystyle V={\frac {1}{3}}\pi r^{2}h.}
Slant height[edit]
The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It is given by {\displaystyle {\sqrt {r^{2}+h^{2}}}} , where {\displaystyle r}  is the radius of the base and {\displaystyle h}  is the height. This can be proved by the Pythagorean theorem.
Surface area[edit]
The lateral surface area of a right circular cone is {\displaystyle LSA=\pi rl}  where {\displaystyle r}  is the radius of the circle at the bottom of the cone and {\displaystyle l}  is the slant height of the cone.^[4] The surface area of the bottom circle of a cone is the same as for any circle, {\displaystyle \pi r^{2}} . Thus, the total surface area of a right circular cone can be expressed as each of the following:

• 
  Radius and height
  

{\displaystyle \pi r^{2}+\pi r{\sqrt {r^{2}+h^{2}}}}
(the area of the base plus the area of the lateral surface; the term {\displaystyle {\sqrt {r^{2}+h^{2}}}}  is the slant height)
{\displaystyle \pi r\left(r+{\sqrt {r^{2}+h^{2}}}\right)}
where {\displaystyle r}  is the radius and {\displaystyle h}  is the height.

• 
  Radius and slant height
  

{\displaystyle \pi r^{2}+\pi rl}
{\displaystyle \pi r(r+l)}
where {\displaystyle r}  is the radius and {\displaystyle l}  is the slant height.

• 
  Circumference and slant height
  

{\displaystyle {\frac {c^{2}}{4\pi }}+{\frac {cl}{2}}}
{\displaystyle \left({\frac {c}{2}}\right)\left({\frac {c}{2\pi }}+l\right)}
where {\displaystyle c}  is the circumference and {\displaystyle l}  is the slant height.

• 
  Apex angle and height
  

{\displaystyle \pi h^{2}\tan {\frac {\theta }{2}}\left(\tan {\frac {\theta }{2}}+\sec {\frac {\theta }{2}}\right)}
where {\displaystyle \theta }  is the apex angle and {\displaystyle h}  is the height.