Conic solids

Conic solids

This animation demonstrates various types of cones and pyramids.

Mathematics

Keywords

conic solid, pyramid, truncated cone, oblique circular cone, right circular cone, face, top, lateral surface, base circle, solid geometry, geometry, mathematics

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Scenes

Consider a geometric shape and a point outside the plane of the geometric shape. Mark a point on the closed curve bordering the geometric shape. Then, draw a line between this point and the previously marked point. Rotate the point marked on the curve around the border of the curve. Meanwhile the point is continually connected with the point marked outside the geometric plane. The surface defined by the rotation of the segment between the two points and the original geometric shape is called a cone.

The original geometric shape is called the base of the cone, the segment between the two points is called generatrix, the surface defined by the generatrices is called lateral surface. The point marked outside the base is called the vertex of the cone.

There are two types of cone-like solids: right cones and oblique cones. If the perpendicular projection of the vertex on the bottom base coincides with the center of the base the cone is a right cone, otherwise it is an oblique cone. If the bottom base of the cone is a circle, the cone is a circular cone.

The lateral surface of the right circular cones is a circle segment whose radius is the height of the lateral surface (the generatrix), while the length of the arc is the perimeter of the base of the cone.

There are two types of cone-like solids: right cones and oblique cones:

If the perpendicular projection of the vertex on the bottom base coincides with the center of the base the cone is a right cone, otherwise it is an oblique cone.

If the bottom base of the cone is a circle, the cone is a circular cone.

Surface area: The surface area of a circular cone is given by the sum of the area of the base and the area of the lateral surface:

Volume: The volume of a straight circular cone is given by one third of the product of the area of the base and the height (h) of the cone:

There are two types of cone-like solids: right cones and oblique cones:

If the perpendicular projection of the vertex on the bottom base coincides with the center of the base the cone is a right cone, otherwise it is an oblique cone.

If the bottom base of the cone is a circle, the cone is a circular cone.

Surface area: The surface area of a circular cone is given by the sum of the area of the base and the area of the lateral surface:

Volume: The volume of a cone is given by one third of the product of the area of the base and the height (h) of the cone:

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