Base of a conic solid
The planar region that forms the widest point of a conic solid; often labeled as the 'bottom' of the conic solid, it determines the exact shape of the conic solid.
It is a 3-D figure with circular base, a vertex not in the plane of the circle, and has a curved surface connecting the base with the vertex. The altitude of the cone is the perpendicular segment that goes from the vertex to the plane containing the circle at the base. The height is the length of the altitude. The slant height is the length of the distance from the vertex to the edge of the base. For a right cone it is necessary that the altitude contains the center of the circle at the base.
The set of points between a point (the vertex) and a non-coplanar region (the base), including the point and the region.
Diameter of a circle (or sphere)
The segment whose endpoints are points on a circle (or sphere) that contains the center of the circle as its midpoint; the length of that segment.
The area of the lateral surface of a solid.
The surface not included in the base (s).
A cone whose axis is perpendicular to the plane containing its base.
The length of a lateral edge of a conic solid
The union of the surface and the region of space enclosed by a 3-D figure; examples: conic solid, cylindrical solid, rectangular solid.
The study of figures in three-dimensional space.
The set of all possible points; made up of infinite planes.
The boundary of a 3-D figure.
The total area of the surface of a solid.
Unit of measuring volume.
Interactive Geometric Applets: Relevant Theorems.
Finding the surface area of cones requires that you know the slant
height, which is the shortest distance from a point in the circumference
in the base to the vertex in the cone. This slant height forms a right
triangle with the radius of the base, and the height of the cone.
Since you have a right triangle, then you may use the Pythagorean
Theorem. This applet presents you the process of finding lateral area,
surface area, and volume for the cone. You may manipulate "r", and "h"
to view different sets of problems.
A cone with a given height, and a given radius has a third of the volume of a cylinder
with that same height, and radius. Play with this applet to verify this volumen relationship.
The formulas are the same, with the only difference that we divide by three the formula
of the cylinder; to get the volume of the cone.
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