Cone

The cone is a solid of revolution generated by a right triangle that rotates around one of its legs.

Components of a Cone

Axis

The axis is the fixed leg about which the triangle turns.

Base

The base is the circle that forms the other leg.

Height

The height is the distance from the apex to the base.

Slant Height

The slant height is the distance from any point on the circumference to the apex of the cone.

Cone

By the Pythagorean theorem, the slant height of the cone is equal to:

Slant Height Formula

Slant Height Formula

Unfold of a Cone

Unfold of a Cone

Lateral Area of a Cone

Lateral Area of a Cone Formula

Surface Area of a Cone

Surface Area of a Cone Formula

Volume of a Cone

Volume of a Cone Formula


Examples

For a party, Louis has made about 10 conical hats out of cardboard. How much cardboard was used in total if each cap has a radius of 15 cm and a slant height of 25 cm?

Cone


Cone Exercise

Cone Solution



Calculate the lateral area, surface area and volume of a cone whose slant height is 13 cm and its base radius is 5 cm.

Cone


Cone Exercise

Cone Operation

Cone Operation

Cone Operation

Cone Solution


Calculate the lateral area, surface area and volume of a cone whose height is 4 cm and its base radius is 3 cm.

Cone


Cone Exercise

Cone Operation

Cone Operation

Cone Operation

Cone Solution