Space Figures

Mr. J. Grossman

Space Figures

Space figures are three-dimensional figures or solids.

Space figures are figures whose points do not all lie in the same plane.

Space figures have depth in addition to width and height.

Common examples: prisms, pyramids, cylinders, cones, and spheres.

Prism

A prism is a polyhedron, with two parallel faces called bases. The other faces are always parallelograms. A prism is named by the shape of its base.

Note: a polyhedron is a solid with flat faces (from Greek poly- meaning "many" and -edron meaning "face"). Each flat surface (or "face") is a polygon.

Prism

A few examples:

Hexagonal Prism Rectangular Prism Triangular Prism

Pyramid

A pyramid is a polyhedron that has 3 or more triangular lateral faces sharing a common vertex. The base of a pyramid may be any polygon.

Square Pyramid Triangular Pyramid

Pyramid

A pyramid has only one base. (The base is the "bottom" of the pyramid.) The other faces are all congruent triangles, and they share a common vertex, which is the top point. The base can be any type of polygon.

Cylinder

A cylinder is a three-dimensional figure having two parallel bases that are congruent circles.

A cylinder is not a polyhedron, because it has a curved, not flat, surface.

Cylinder

Cone

A cone is a three-dimensional figure with one vertex and a circular base.

Sphere

A sphere is a space figure having all of its points the same distance from its center. The distance from the center to the surface of the sphere is called its radius. Any cross-section of a sphere is a circle.

A sphere is perfectly symmetrical. It has no edges or vertices. It is not a polyhedron.

Sphere

A ball is shaped like a sphere, as is the Earth. A hemisphere is "half of a sphere;" that is, either of the two parts into which the sphere is divided by its equator (or by any circle on the sphere with its center at the center of the sphere).

Geometry Nets

A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape.

The net of a three-dimensional object is a representation of its faces in two dimensions.

A solid may have different nets.

Geometry Nets Examples

The following nets can be folded along the dotted lines to form cubes.

Geometry Nets Examples

A rectangular prism is formed by folding a net as shown:

Geometry Nets Examples

Net of a rectangular pyramid

Geometry Nets Examples

The net of a cylinder consists of three parts:

One circle gives the base and another circle gives the top.

A rectangle gives the curved surface.

Geometry Nets Examples

The net of a cone consists of the following two parts:

a circle that gives the base; and

a sector that gives the curved surface

Any questions?

Euclid was a Greek mathematician, who was also called Euclid of Alexandria. To a lot of folks he is the “Father of Geometry”. He lived around 300bc.