Surface Area and Volume of Similar Figures

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Honors Geometry Section 8.6 Areas and Volumes of Similar Figures

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Presentation transcript:

Surface Area and Volume of Similar Figures

Definition A polyhedron is a solid that is bounded by polygons.

Tell whether each figure below is a polyhedron.

Definition Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii, are called similar solids.

Tell whether each given right rectangular prism is similar to the right rectangular prism shown below.

Similar Solids Theorem If two similar solids have a scale factor of a : b, then corresponding areas (and surface areas) have a ratio of a2 : b2 and corresponding volumes have a ratio of a3 : b3.

The pyramids are similar The pyramids are similar. Pyramid P has a volume of 1000 cubic inches and Pyramid Q has a volume of 216 cubic inches. Find the scales factor of Pyramid P to Pyramid Q.

Solid I is similar to Solid II Solid I is similar to Solid II. Find the scale factor of Solid I to Solid II.

Assignment pg. 850 #3-23 all