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# Cone

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#### Anton

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 altitude of the cone, that is, the distance from the vertex to the center of the base. So 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 perimeter of the cone 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

PLANETCALC, Cone