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11.1 – Solid Figures

11.1 – Solid Figures. Solid Figures. Three-dimensional shapes are called solids . When a solid is formed by polygons, it is called a polyhedron . Prisms and Pyramids are examples of polyhedra . To name a prism or pyramid, use the shape of the base . Examples of Polyhedra.

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11.1 – Solid Figures

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  1. 11.1 – Solid Figures

  2. Solid Figures • Three-dimensional shapes are called solids. • When a solid is formed by polygons, it is called a polyhedron. • Prisms and Pyramids are examples of polyhedra. To name a prism or pyramid, use the shape of the base.

  3. Examples of Polyhedra Prisms have two bases. Pyramids have one base.

  4. Parts of a Polyhedron • The plane surfaces are called faces. • The segments joining vertices are called edges. What shape are the bases?

  5. Types of Solids Cube (Square Prism) Rectangular Prism Triangular Prism

  6. Types of Solids Rectangular Pyramid Triangular Pyramid Pentagonal Pyramid

  7. Types of Solids Cylinder Cone Sphere

  8. 11.2 – Surface Areas of Prisms and Cylinders

  9. Lateral Faces • The lateral faces of a prism are the faces of the prism that are not bases. • Lateral area is the sum of the area of the lateral faces.

  10. Surface area of a Prism • Another way to find the surface area of a prism is to use the method developed from the activity.

  11. Surface Area of a Cylinder • A cylinder is a solid with two congruent circular bases that lie in parallel planes. The lateral area of a cylinder is the area of the curved surface.

  12. Surface Area of the Cylinder

  13. 11.3 – Surface Areas of Pyramids and Cones

  14. Pyramids • The Rainforest Pyramid on Galveston Island in Texas is one example of how pyramids are used in architecture. • The base of a pyramid is a polygon and the lateral faces are triangles with a common vertex.

  15. Defining the Parts of a Pyramid

  16. Surface Area of a Cone • A cone has a circular base and a vertex that is not in the plane as the base.

  17. 11.4 – Volume of Prisms and Cylinders

  18. Volume • The amount of water in an aquarium is an example of volume. The volume of a solid is the number of cubic units contained in its interior.

  19. Volume of a Prism

  20. Volume of a Cylinder • The method for finding the volume of a cylinder is the same for finding the volume of a prism.

  21. 11.5 – Volume of Pyramids and Cones

  22. 11.6 – Surface Area and Volume of Spheres

  23. Spheres • A globe is an example of a sphere. A sphere is the set of all points in space that are the same distance from a point, the center of the sphere. • A geometric plane passing through the center of a sphere divides it into two hemispheres. The globe is divided into the Northern Hemisphere and the Southern Hemisphere.

  24. Some websites that may be helpful: http://www.learner.org/interactives/geometry/area_surface.html https://www.khanacademy.org/math/geometry/basic-geometry

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