10.1 Intro to 3-Dimensional Figures 3-D Figure traits: length, width, and height; face is a flat surface; edge is where 2 faces meet. Polyhedron: 3-D figure whose faces are all polygons; vertex is the point where 3 or more edges meet; base is the face that is used to name the type of polyhedron. Prism: Polyhedron with 2 parallel congruent bases of any type polygon, other faces are parallelograms.

10.1 Intro to 3-Dimensional Figures 3-D Figure traits: length, width, and height; face is a flat surface; edge is where 2 faces meet. Polyhedron: 3-D figure whose faces are all polygons; vertex is opposite of the base and is the point where 3 or more edges meet; base is the face that is used to name the type of polyhedron. Pyramid: Polyhedron with 1 base of any type polygon, other faces are triangles.

10.1 Intro to 3-Dimensional Figures Other 3-D figures: not all faces are polygons. Cylinder: 2 parallel, congruent circles for the bases, and a curved plane that connects the two bases Cone: 1 base that is a circle, and a curved surface that comes to a point at the vertex, opposite of the base.

10.1 Intro to 3-Dimensional Figures Other 3-D figures: not all faces are polygons. Sphere: Surface made up of points that are the same distance from a given point at the center (3-D circle)

10.2 Volume of Prisms and Cylinders Volume: number of congruent cubes needed to fill a 3-D figure. Rectangular Prism: V= area of the base × height (length × width) × height (l × w) × h = B × h Triangular Prism:V=area of the base × height (½ × base × height t ) × height (½ × b × h t ) × h = B × h Cylinder: V=area of the base × height πr 2 × height πr 2 × h = B × h B is the area of the base (polygon or circle).

10.3 Volume of Pyramids and Cones Rectangular Pyramid: V=1/3 × area of the base × height 1/3 × (length × width) × height 1/3 × (l × w) × h = 1/3Bh Triangular Pyramid:V=1/3 × area of the base × height 1/3 × (½ × base × height t ) × height 1/3 × (½ × b × h t ) × h = 1/3Bh Cone: V=1/3 × area of the base × height 1/3 × πr 2 × height 1/3 × πr 2 × h = 1/3Bh B is the area of the base (polygon or circle).

10.4 Surface Area of Prisms and Cylinders Imagine disassembling a figure at its vertices and edges, completely flattening it, and measuring the areas. Prism: Surface area is for the 2 bases (2B) and the area of the parallelograms (P B h), where P is the perimeter of the base. S = 2B + P B h

10.4 Surface Area of Prisms and Cylinders Cylinder: Surface area is for the 2 bases (area of 2 circles or 2πr 2 ) and the area of the flattened side (circumference of circle times the height or 2πrh) S = 2πr 2 + 2πrh

10.5 Surface Area of Pyramids and Cones Pyramid: Surface area is for the base of a polygon (B or l × w) and the areas of each of the congruent isosceles triangles (1/2bh), in this case the b for each triangle is replaced by P (the perimeter of the the base), and the h is replaced by l (little letter “el”), the slant height of the triangles. S = B + L = l × w + ½P l = l × w + ½ × 4 × b × l = l × w + 2 × b × l = l × w + 2b l

10.5 Surface Area of Pyramids and Cones Cone: Surface area is for the base of the cone (B or πr 2 ) and lateral area of the cone (L or πr l ), where the l (little letter “el”) is the slant height. S = B + L = πr 2 + πr l = π(r 2 + r l)

10.6 Changing Dimensions (Scale to a Whole New Dimension!!!) Imagine that you have a Rubric’s Cube that 3 inches by 3 inches by 3 inches. Imagine further that I tell you that your cube is actually a 1/4 model of the original cube. That means that the real Rubric’s cube would be 12 inches or 1 foot tall. (3/x = 1/4). What does that mean in terms of the area and volume? ModelActual Area3 × 3 = 9 in × 12 = 144 in. 2 Volume3 × 3 × 3 = 27 in × 12 × 12 = 1,728 in. 3 1 dimension rule:model × scale factor = actual Area Rule:model × ___________= actual Volume Rule:model × ___________= actual