Geometry Lesson 1 7 ThreeDimensional Figures Objective Identify

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

Polyhedrons l 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 Pyramid Rectangular Pyramid Pentagonal Pyramid

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, MRQP, RSTQ, Remember to include the bases RSNM, STON, PQTO 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: Faces: GHI & GHKJ, JKL HKLI, & Vertices: G, H, K, J, L, I GJLI

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

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 l 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 l Surface Area (Total Area) l Volume l

Find Surface area and Volume Square Pyramid Surface area (Total Area): write formula first Find P and B first P = 4(6) = 24 B = 6*6 = 36 Plug into formula = 96 cm 2 Continued…

Continued…Volume Remember B = 36 = 48 3 cm

Find Surface area & Volume 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) = 286. 4 cm 2 V = Bh = (52)(6) = 312 cm 3

Find the Surface Area & Volume 1507. 96 rounded up to 1508. 0 1884. 95 rounded up

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