**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

**Related items**

### 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:

### Related items

#### Conic sections

The conic section is a plane curve that is created when a right circular cone is intersected by a plane.

#### Cylindrical solids

This animation demonstrates various types of cylindrical solids as well as their lateral surfaces.

#### Perimeter, area, surface area and volume

This animation presents the formulas to calculate the perimeter and area of shapes as well as the surface area and volume of solids.

#### Platonic solids

This animation demonstrates the five regular three-dimensional (or Platonic) solids, the best known of which is the cube.

#### Ratio of volumes of similar solids

This 3D scene explains the correlation between the ratio of similarity and the ratio of volume of geometric solids.

#### Solids of revolution (rectangle)

Rotating a rectangle around its axes of symmetry or around its sides results in solids of revolution.

#### Sphere

A sphere is the set of points which are all within the same distance from a given point in space.