# Cone

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#### Timur

• Article : Cone - Editor
Created: 2008-11-15 09:09:48, Last updated: 2021-03-05 16:50:19

Cone is a three-dimensional figure that has one circular base and one vertex (apex).

An oblique cone is a cone with an apex that is not aligned above the center of the base.
A right cone is a cone in which the apex is aligned directly above the center of the base. The base need not be a circle here.

The volume of both right cone and oblique cone is $V=\frac{1}{3}S_bH$, where $S_b$ is a surface area of cone base.

When the base of a right cone is a circle, it is called a right circular cone.
Such a cone is characterized by the radius of the base and the cone's altitude, that is, the distance from the vertex to the center of the base. So the volume of a circular cone is $V=1/3\pi R^2H$

The slant height of such a cone is the length of a straight line drawn from any point on the cone's perimeter to the vertex.
If the radius of the base is R and the altitude of the cone is H, then the slant height is $H_s= \sqrt{R^2+H^2}$
Now we can calculate total surface area of a right circular cone: $S=S_{base} + S_{lateral}=\pi R^2 + \pi R H_s=\pi R^2 + \pi R \sqrt{R^2+H^2}$

#### Cone

Digits after the decimal point: 5
Volume

Lateral surface area

Surface area

A frustum of cone is a truncated cone in which the plane cutting off the apex is parallel to the base.
Volume of a right circular cone frustum is $V=\frac{1}{3}\pi (R_1^2+R_1 R_2 + R_2 ^2)H$
Surface area of a right circular cone frustum is $S=\pi R_1^2 + \pi R_2^2 + \pi (R_1+R_2)\sqrt{(R_1-R_2)^2 + H^2}$

#### Cone frustum

Digits after the decimal point: 5
Volume

Lateral surface area

Surface area

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