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The area of a rotating cone

Definition:

The round cone or rotating cone is a geometrical solid obtained by rotation of a right triangle around its leg.

The area of a rotating cone is the sum of the areas of lateral and base.

The area of a lateral of a rotating cone (conic surface) is the product of the Pi value and radius of the circumference of cone’s base and its lateral length (the distance between the cone’s apex and a point from the circumference described by its base.

The area of a lateral of a rotating cone

Computing relationship:

where:

C — the circumference of a base;

r — the rotation radius, base radius;

l — the slant height of a cone.

Calculator: the area of a lateral of a rotating cone


For separation of number integers and decimals, use the symbol – point [.]

the rotation radius, base radius — r

the slant height of a cone — l

 


the area of a lateral of a rotating cone =

 

Total area of a rotating cone

Computing relationship:

where:

r — the rotation radius, base radius;

l — the slant height of a cone.

Calculator: total area of a rotating cone


For separation of number integers and decimals, use the symbol – point [.]

the rotation radius, base radius — r

the slant height of a cone — l

 


the area of a lateral of a rotating cone =

 

 

context information: contemporary and archaic unit of measurement of area