SOLID GEOMETRY

Solid Geometry is the geometry of three-dimensional space, the kind of space we live in ...

Three Dimensions

It is called three-dimensional, or 3D because there are three dimensions: width, depth and height.

Two main types of solids

Polyhedron

Non-polyherdon

Polyhedra

A polyhedron is a solid made of flat surfaces. Each surface is a polygon. Examples:

1. Platonic solids -

tetrahedron

Cube (hexahedro

n)

octahedron

dodecahedron icosahedron

polyhedra

2. Prisms - A prism has the same cross section all along its length !

Square prismTriangular prism

Pentagonal prism

Pyramids

Pyramids - a solid shape or structure that has triangular sides that slope to meet in a point and a base that is often, but not necessarily, a square

Parts of pyramid

A pyramid is made by connecting a base to an apex

Types of pyramid

TriangularPyramid

Pyramid Base

SquarePyramid:

PentagonalPyramid:

Non Polyhedra

Non polyhedra- Some solids have curved surfaces, or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:

1. Sphere2. Cylinder3. Torus4. Cone

sphere

Sphere -a three-dimensional closed surface consisting of all points that are a given distance from a center

Properties:1. It is perfectly

symmetrical2. It has no edges or

vertices3. All points on the surface

are the same distance from the center

cylinder

Cylinder – an object or shape with straight sides and circular ends with equal size It has a flat base and a flat topThe base is the same as the top, and also in-betweenIt has one curved side

Because it has a curved surface it is not a polyhedron.

Torus

Torus- a ring shaped surface

It can be made by revolving a small circle along a line made by another circle.It has no edges or verticesIt is not a polyhedron

Cone

Cone- has a circular based and tapers to a point at the top or has a circular top and tapers to a point at the bottom.

It has a flat base

It has one curved side

Because it has a curved surface it is not a polyhedron.

Prepared by:

NEIL B. MEMITA Teacher III San Isidro High School Lupao, Nueva Ecija Philippines