Cone facts for kids

A cone is a 3D shape that looks like a party hat or an ice cream cone. You can imagine making a cone by spinning a right triangle (a triangle with a 90-degree angle) around one of its shorter sides. That spinning side becomes the cone's central line, called its axis. The flat, round bottom part is called the base. The pointy top is called the apex or vertex. If something is shaped like a cone, we say it is conical.

A cone, marked with its height (h) and radius (r)

What is a Cone?

A cone is a solid shape. It has a flat base and a curved side that tapers (gets narrower) to a single point called the apex or vertex. Think of an ice cream cone before you add the ice cream!

Parts of a Cone

• Base: This is the flat bottom part of the cone. For a common cone, the base is a circle.
• Apex (or Vertex): This is the single pointy top of the cone.
• Axis: This is an imaginary line that goes from the apex straight down to the center of the base.
• Height (h): This is the distance from the apex to the center of the base, measured along the axis.
• Radius (r): This is the distance from the center of the circular base to its edge.
• Slant Height: This is the distance from the apex to any point on the edge of the base, along the curved surface.

Different Kinds of Cones

There are a few ways cones can be different:

• Right Circular Cone: This is the most common type. Its axis is at a 90-degree angle to the center of its circular base. It looks perfectly symmetrical.
• Oblique Cone: In an oblique cone, the axis is not at a 90-degree angle to the base. This makes the cone look tilted or leaning.
• Double Cone: Imagine two cones joined at their apexes. This is a double cone. It extends infinitely in both directions if we consider it made of lines. Each half is called a nappe.

How to Find the Volume of a Cone

The volume of a cone is how much space it takes up. To find the volume of a cone, you need to know the area of its base and its height.

The formula for the volume of a cone is:

Let's break it down:

• V stands for Volume.
• A_B stands for the Area of the Base. If the base is a circle, its area is found using the formula: Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): A_B = \pi r^2 (where is approximately 3.14159, and is the radius of the base).
• h stands for the height of the cone.

So, if you have a circular base, the formula becomes:

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): V = \frac{1}{3}\pi r^2 h.

This means a cone's volume is one-third of the volume of a cylinder that has the same base and height.

Related pages

• Conic section

Images for kids

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  A right circular cone and an oblique circular cone

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  A double cone

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  An illustration from 1734 showing geometric problems.

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  An elliptical cone, where the base is an ellipse instead of a circle.

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  In projective geometry, a cylinder can be seen as a cone whose apex is infinitely far away.

See also

In Spanish: Cono (geometría) para niños