A metal sphere of radius 6 in. is melted down and recast as a solid cone with the same radius. What is the lateral area of the cone? 12-5: Areas and Volumes of Similar Solids Formulas: β’ Prisms: β π½ = π©π β π». π¨. = ππ© + ππ β’ Pyramids: π π β π½ = π©π β π». π¨. = π© + π ππ π β’ Cylinders: β’ π½ = π ππ π β’ π». π¨. = ππ ππ + ππ ππ β’ Cones: π β’ π½ = π ππ π π β’ π». π¨. = π ππ + π ππ β’ Spheres: β’π½= β’π¨= π π ππ π ππ ππ Comparing Similar Solids If the scale factor of two similar solids is π: π 1. The ratio of the corresponding perimeters (or any lengths) is π: π 2. The ratio of the base areas, lateral areas, and total areas is ππ : ππ 3. The ratio of the volumes is ππ : ππ True or false 1. All spheres are similar. 2. All right cylinders are similar. 3. All cubes are similar. 4. Two cones have base radii 9 m and 12 m, and heights 12 m and 18 m respectively. The cones are similar. Two similar cylinders have circumferences of 18π ππ and 24π ππ. What is the ratio of their volumes? Two similar square pyramids have base areas 4 π2 and 36 π2 . 1. Find the ratio of the heights of the pyramids 2. If the height of the larger pyramid is 27 π, what is the height of the smaller pyramid? Two similar cones have volumes of 16 ππ3 and 54 ππ3 . If the lateral (slant) height of the smaller cone is 8 ππ, what is the lateral (slant) height of the large one? p. 511: #1-17 odd, 12, 18 Chapter 12 on Friday!!!
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