Chapter 10 Study Guide / Review Section1: Solid Geometry 3-D Figures / Terminology See Chart Page 654 – Name Classify Solids Recognize Cross Sections – Nets Section2: Representations of 3-D Figures Orthographinc Drawings – Isometric Drawings 1 & 2 Point Perspectives Section 3: Formulas in 3-D Polyhedron Euler’s Formula: V – E + F = 2 Graphing in 3-D Ordered Triple (x, y, z) Finding the Diagonal of a Right Prism Distance AND Midpoint in 3-D
HELPFUL FORMULAS A(Triangle) = ½ b∙h A(Rectangle) = lw OR b∙h A(Circle) = ᴫ∙r2 C(Circle) = ᴫ∙d OR 2∙ᴫ∙r A(Reg Poly) = ½ aP A(Pointed Part) = ᴫ∙r∙l A(Rectangle “chunk”) = (2∙ᴫ∙r)∙h
Section 4: Surface Area of Prisms & Cylinders
*ACCOUNT FOR ALL SURFACES* Utilize the Two-Dimensional Formulas from Chapter 9 Surface Area vs. Lateral Area (ALL Surfaces vs. Everything BUT the Bases) Section 5: Surface Area of Pyramids & Cones PYRAMID SA: = 1 Rect. Base + 4 Triangle Faces LA: Just the Triangle Faces CONE SA: = 1 Circle Base + 1 “Pointed Part” (ᴫ∙r∙l) LA: Just the Pointed Part (ᴫ∙r∙l) Section 6: Volume of Prisms & Cylinders V = B∙h (h = Altitude) B = Area of the 2-D Base Cavilieri’s Principle Section 7: Volume of Pyramids & Cones Bh V= (Pretend that the Pyramid / Cone is a Prism or Cylinder then Divide by 3) 3 Utilize the Two-Dimensional Formulas from Chapter 9 Section 8: Volume / Surface Area of Spheres (Hemispheres) 4 r3 V SPH = Remember: The “Great Circle” 3 SASPH: 4∙ᴫ∙r2 Hemisphere = ½ Sphere: V HEMI: Total Volume of Sphere divided by 2 SA HEMI : 3∙ᴫ∙r2 (2 “Great Circles” to cover dome + 1 to cover bottom)