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Surface Areas and Volumes of 3D Shapes: Complete Guide Review

Explore the formulas and steps to find surface areas and volumes of prisms, cylinders, pyramids, cones, and composite solids. Learn to solve problems and identify missing pieces with examples. Discover how to work with regular polygons, central angles, triangle trigonometry, and composite shapes. Enhance your understanding of geometry concepts.

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Surface Areas and Volumes of 3D Shapes: Complete Guide Review

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  1. 11.7A (11.4 – 11.7 Review) Prisms, Cylinders, Pyramids, Cones and Composite Solids: Surface Areas and Volumes Regular Polygons: A = ½ aP Central Angle/Triangle Trig!

  2. Right Prisms and Cylinders: Flat-Tops Rt Cylinder Lateral Surface Area: L = Ph P is the Perimeter of the Base, h is the height Surface Area: S = L + 2B B is Area of the Base Volume: V = Bh

  3. Right Pyramids and Cones: Pointy-Tops l h r Right Cone

  4. Steps to Solving Problems: 1. Is it Flat, Pointy or both? 2. Write Formulas – be careful! 3. Draw the Base: find P, B, h, and l as needed. 4. Substitute into equation & answer the question.

  5. Finding Missing Pieces: 1. Given a square base pyramid, l = 13, s = 10, find L, S and V 2. Find L, S and V of the cone with r = 8, slant height = 10.

  6. Composite Solids: 1. Find S and V 12 2. Find S and V if the cylinder is removed from the prism.

  7. Using Equations: • Find the surface area of a cone with • h = 6 ft and V = 200 ft3 • Find the volume of a cylinder with a surface • area of 240 m2 and a height of 7 m

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