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

Polyhedrons Polyhedrons Face – each flat surface 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

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

Naming Prisms Triangular Prism Rectangular Prism

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

Naming Pyramids Triangular Rectangular Pyramid Pyramid Pentagonal

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

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

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.

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. Faces: MNOP, RSTQ, MRQP, RSNM, STON, PQTO Remember to include the bases Edges: Vertices: R, M, S, N, T, O, Q, P

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

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

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

Regular Polyhedrons: Platonic Solids

Regular Polyhedrons: Platonic Solids

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.

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

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…

Continued…Volume Remember B = 36 = 48 cm3

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

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

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

The diameter of the pool Mr. Sato purchased is 8 feet 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

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