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12-5 Areas and Volumes of Similar Solids

Learn about rules, ratios, and calculations for similar solids using a scale factor of 2:3. Explore examples with cones and practice problems. Get ready for tomorrow's quiz!

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12-5 Areas and Volumes of Similar Solids

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  1. 12-5 Areas and Volumes of Similar Solids

  2. Rules • Scale Factor – 2:3 • Also used for: dimensions (radius, length, slant height, base edge, etc.), perimeter/circumference • Ratio of Areas –(2:3)2 4:9 • NEW!! Ratio of Volumes –(2:3)3 8:27 • Remember: If 2 Solids have the same scale factor, Then they are similar

  3. EXAMPLE • The circumferences of 2 similar cones are 8π and 6π. • What is the scale factor? • Ratio of diameters? • Ratio of heights? • Ratio of lateral areas? • Ratio of base areas? • Ratio of volumes? 4:3 4:3 4:3 16:9 16:9 64:27

  4. For Same 2 Cones • If you know the slant height of the first cone is 24, what is the slant height of the second cone? 4/3 = 24/x Cross Multiply: Watch the Whiteboardl=18 • If the total area of the 2nd cone is 36π, what is that total area of the 1st cone? 16/9 = x/36π x = 64π *Watch me on the Whiteboard

  5. TOO • The ratio of Volumes for 2 solids is 125:64, • Find: • A) Scale Factor • B) Ratio of Areas • C) Ratio of perimeters Answers: a) 5:4 b) 25:16 c) 5:4

  6. Homework • Page 511 #1-8, 11 • Pg. 496 Self Test 1-6, skip 4 QUIZ Tomorrow!!

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