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Understanding Areas and Volumes of Similar Figures in Geometry

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This section explores the concepts of area and volume in similar figures, including rectangular prisms and spheres. It introduces the Area Proportionality Theorem, which states that two similar figures with corresponding linear measures in a ratio have areas in the square of that ratio. Additionally, it covers the Volume Proportionality Theorem, highlighting that volumes are in the cube of the ratio of corresponding linear measures. Examples provided illustrate finding perimeter, area, and volume ratios for similar shapes, enhancing comprehension of geometric relationships.

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Understanding Areas and Volumes of Similar Figures in Geometry

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  1. Honors Geometry Section 8.6Areas and Volumes of Similar Figures

  2. Each pair of figures below is similar.

  3. Each pair of figures below is similar.

  4. Each pair of figures below is similar.

  5. Area Proportionality TheoremTwo similar figures with corresponding linear measures in the ratio have areas in the ratio__________.

  6. Consider two similar rectangular prisms (a box) with dimensions of 9, 12, 6 and 6, 8, 4.scale factor = __________ratio of volumes = __________ (V = l w h)

  7. Consider two spheres with radii 10 and 5. scale factor = __________ ratio of volumes = __________

  8. Volume Proportionality Theorem Two similar figures with corresponding linear measures in the ratio have volumes in the ratio

  9. Examples: The ratio of corresponding base edges in two similar pyramids is 3:5.a) Find the ratio of the perimeter of the bases. (Linear? Area? Volume?)b) Find the ratio of the area of the bases.c) Find the ratio of the volumes of the pyramids.

  10. Examples: The ratio of corresponding base edges in two similar pyramids is 3:5.d) If the perimeter of the base in the first pyramid is 36cm, find the perimeter of the base in the second pyramid.

  11. Examples: The ratio of corresponding base edges in two similar pyramids is 3:5.e) If the second pyramid has a volume of 80cm3, find the volume of the first pyramid.

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