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Calculating Volumes of Triangular Prisms and Cylinders: Exploring Formulas and Shapes

Learn and understand the formulas for finding the volume of triangular prisms and cylinders, and compare them to the formula for rectangular solids. Explore the vocabulary of polyhedrons, faces, edges, vertices, cubes, and bases.

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Calculating Volumes of Triangular Prisms and Cylinders: Exploring Formulas and Shapes

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  1. California Standards Preparation for MG1.3 Know and usethe formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.

  2. Vocabulary polyhedron face edge vertex cube base

  3. A polyhedron is a three-dimensional object with flat surfaces, called faces, that are polygons. When two faces of a three-dimensional figure share a side, they form an edge. A point at which three or more edges meet is a vertex (plural: vertices). A cube is formed by 6 congruent square faces. It has 8 vertices and 12 edges.

  4. 5 faces 8 edges 5 vertices 7 faces 15 edges 10 vertices Additional Example 1: Identifying Faces, Edges, and Vertices Identify the number of faces, edges, and vertices on each three-dimensional figure. A. B.

  5. 6 faces 12 edges 8 vertices 5 faces 9 edges 6 vertices Check It Out! Example 1 Identify the number of faces, edges, and vertices on each three-dimensional figure. A. B.

  6. Two types of polyhedrons are prisms and pyramids. Prisms and pyramids are named for the shape of their bases. A base of a three-dimensional figure is a face by which the figure is measured or classified.

  7. Helpful Hint The bottom face of a prism is not always one of its bases. For example, the bottom face of the triangular prism in Example 1 is not one of its triangular bases.

  8. Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because their surfaces are not polygons.

  9. The figure is not a polyhedron. There is a curved surface. The figure represents a cylinder. There are two congruent, parallel bases. The bases are circles. Additional Example 2A: Naming Three-Dimensional Figures Name the three-dimensional figure represented by the object.

  10. The figure is a polyhedron. All the faces are flat and are polygons. The figure is a triangular pyramid. There is one base and the other faces are triangles that meet at a point, so the figure is a pyramid. The base is a triangle. Additional Example 2B: Naming Three-Dimensional Figures Name the three-dimensional figure represented by the object.

  11. The figure is a polyhedron. All the faces are flat and are polygons. The figure is a rectangular prism. There are two congruent, parallel bases, so the figure is a prism. The bases are rectangles. Additional Example 2C: Naming Three-Dimensional Figures Name the three-dimensional figure represented by the object.

  12. The figure is a polyhedron. All the faces are flat and are polygons. The figure is a square pyramid. There is one base and the other faces are triangles that meet at a point, so the figure is a pyramid. The base is a square. Check It Out! Example 2A Name the three-dimensional figure represented by the object.

  13. The figure is a polyhedron. All the faces are flat and are polygons. The figure is a rectangular prism. There are two congruent, parallel bases, so the figure is a prism. The bases are rectangles. Check It Out! Example 2B Name the three-dimensional figure represented by the object.

  14. The figure is not a polyhedron. There is a curved surface. The figure represents a cylinder. There are two congruent, parallel bases. The bases are circles. Check It Out! Example 2C Name the three-dimensional figure represented by the object.

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