Honors Geometry Section 8.6 Areas and Volumes of Similar Figures

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Honors Geometry Section 8.6 Areas and Volumes of Similar Figures

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Presentation transcript:

Honors Geometry Section 8.6 Areas and Volumes of Similar Figures

Each pair of figures below is similar.

Each pair of figures below is similar.

Each pair of figures below is similar.

Area Proportionality Theorem Two similar figures with corresponding linear measures in the ratio have areas in the ratio __________.

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)

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

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

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.

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.

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.