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Identifying and Measuring Three-Dimensional Figures

Learn how to identify and name different three-dimensional figures, find their surface area and volume, and understand the properties of polyhedrons, prisms, pyramids, cylinders, cones, and spheres.

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Identifying and Measuring Three-Dimensional Figures

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  1. Geometry Lesson 1 – 7 Three-Dimensional Figures Objective: Identify and name three-dimensional figures. Find surface area and volume.

  2. Polyhedrons • Polyhedrons • A solid with all flat surfaces that enclose a single region of space. • Face – each flat surface • Edges – the line segment where the faces intersect • Vertex – the point where 3 or more edges intersect

  3. Types of Solids:Prism • A polyhedron with 2 parallel and congruent faces called bases • Bases are connect by parallelogram faces This is one example of a prism Named using the bases: Pentagonal Prism

  4. Naming Prisms Triangular Prism Rectangular Prism

  5. Types of Solids:Pyramid • A polyhedron that has a polygonal base and three or more triangular faces that meet at a common point. One example: Rectangular Pyramid

  6. Naming Pyramids Triangular Pyramid Rectangular Pyramid Pentagonal Pyramid

  7. Types of Solids:Cylinder • Not a polyhedron • A solid with congruent parallel circular bases connected by a curved surface.

  8. Types of Solids:Cone • Not a polyhedron • A solid with a circular base connected by a curved surface to a single vertex.

  9. Types of Solids:Sphere • Not a polyhedron • A set of points in space that are the same distance from a given point. A sphere has no faces, edges, or vertices.

  10. Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices. Yes a polyhedron Bases: MNOP & RSTQ *Use the ‘top’ and ‘bottom’ on Rectangular prisms for the bases. Remember to include the bases Faces: MNOP, RSTQ, MRQP, RSNM, STON, PQTO Edges: Vertices: R, M, S, N, T, O, Q, P

  11. Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices. Not a polyhedron

  12. Determine whether the solid is a polyhedron, if yes, name the bases, faces, edges, and vertices. Bases: GHI & JKL Faces: GHKJ, HKLI, & GJLI Vertices: G,H,K,J,L,I

  13. Regular Polyhedron • A polyhedron with all faces regular polygons and all edges congruent. Can you think of a regular polygon?

  14. Regular Polyhedrons:Platonic Solids

  15. Regular Polyhedrons:Platonic Solids

  16. Area & Volume • Lateral Area – area of the lateral faces (faces that are not bases) • Surface Area (Total Area)– is the area of the whole figure • Lateral area + area of bases • Volume – the measure of the amount of space enclosed by a solid figure.

  17. Hands-on Activity • Using the geometric solids set • Find formulas for the following for all solids • Lateral Area • Surface Area (Total Area) • Volume

  18. Find Surface area and Volume • Square Pyramid Surface area (Total Area): write formula first Find P and B first P = 4(6) = 24 = 96 cm2 B = 6*6 = 36 Plug into formula Continued…

  19. Continued…Volume Remember B = 36 = 48 cm3

  20. Find Surface area & Volume Need to have both! Need to have both!

  21. Find Surface Area & Volume P = 2(5.2) + 2(10) = 30.4 B = (5.2)(10) = 52 T = (30.4)(6) + 2(52) V = Bh = 286.4 cm2 = (52)(6) = 312 cm3

  22. Find the Surface Area & Volume 1884.95 rounded up 1507.96 rounded up to 1508.0

  23. The diameter of the pool Mr. Sato purchased is 8 feet. The height of the pool is 20 inches. Find each measure to the nearest tenth. • Surface Area of pool *Be careful dealing with feet and inches! We don’t need 2 bases since the pool Does not have a top 20 inches is 1 2/3 feet

  24. Be careful with feet and inches! • Volume of water needed to fill the pool to a depth of 16 inches. 16 inches is 1 1/3 feet

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