Calculate volume, total surface area, lateral area and slant height of a right cone.
A right circular cone has volume (1/3)πr²h — exactly one-third of the cylinder with the same base and height. The slant height l = √(r²+h²).
Volume
V = (1/3)πr²h
Lateral Area
LA = πrl
This can be proven via calculus (integration of circular cross-sections) or Cavalieri's principle.
Height = √(l² − r²). The slant height, radius and height form a right triangle.