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Solid geometry
Solid geometry describes three-dimensional space and includes two main types of solids: polyhedra and non-polyhedra. Polyhedra are solids made of flat surfaces that are polygons, such as cubes, pyramids, and spheres. Non-polyhedra have curved surfaces, such as cylinders, cones, and toruses. Solid geometry examines properties of three-dimensional shapes, including their dimensions, parts, and distinguishing characteristics.
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Solid geometry involves the study of three-dimensional space, exploring the properties of solids.
Three-dimensional space includes width, depth, and height, fundamental characteristics of solids.
Solids are categorized into two main types: polyhedra and non-polyhedra, based on surface types.
Polyhedra consist of flat polygon surfaces. Examples include Platonic solids like cubes and tetrahedra.
Prisms maintain a consistent cross-section along their length, with examples like square and triangular prisms.
Pyramids have sloping triangular sides that converge at a point with a base, can vary in shape.
A pyramid is formed by connecting a base to an apex, defining its structure.
Different types of pyramids include triangular and square pyramids, distinguished by their base shapes.
Non-polyhedra have curved or mixed surfaces. Examples include spheres, cylinders, and cones.
A sphere is a symmetrical three-dimensional shape with no edges or vertices, all points equidistant from the center.
A cylinder has straight sides and circular ends, featuring a flat base and a single curved side.
A torus is a ring-shaped surface, generated by revolving a small circle along a line made by another circle.
A cone has a circular base tapering to a point, with one curved side, and is not a polyhedron.
Presented by Neil B. Memita from San Isidro High School, highlighting the educational context of the material.
Solid geometry
- 1. Solid geometrySolid Geometryis the geometry of three-dimensional space, the kind of space we live in ...
- 2. Three DimensionsIt iscalled three-dimensional, or 3D because there are three dimensions: width, depth and height.
- 3. Two main typesof solidsPolyhedronNon-polyherdon
- 4. PolyhedraA polyhedron isa solid made of flat surfaces. Each surface is a polygon. Examples:Platonic solids -tetrahedronCube (hexahedron)octahedrondodecahedronicosahedron
- 5. polyhedra2. Prisms -A prism has the same cross section all along its length !Square prismTriangular prismPentagonal prism
- 6. PyramidsPyramids - asolid 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
- 7. Parts of pyramidApyramid is made by connecting a base to an apex
- 8. Types of pyramidPyramidBaseTriangularPyramidSquarePyramid:
- 9. Non PolyhedraNon polyhedra-Some solids have curved surfaces, or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:SphereCylinderTorusCone
- 10. sphereSphere -a three-dimensionalclosed surface consisting of all points that are a given distance from a centerProperties:It is perfectly symmetricalIt has no edges or verticesAll points on the surface are the same distance from the center
- 11. cylinderCylinder – anobject 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 sideBecause it has a curved surface it is not a polyhedron.
- 12. Torus Torus- a ring shaped surfaceIt 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
- 13. Cone Cone- hasa 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 baseIt has one curved sideBecause it has a curved surface it is not a polyhedron.
- 14. Prepared by:NEIL B.MEMITATeacher IIISan Isidro High SchoolLupao, Nueva EcijaPhilippines