Double the dimensions, quadruple the surface area. Pairs build similar prisms and compare the ratios of their surface areas and volumes to the ratio of the heights. Given two similar cones, partners determine the ratios of the lateral areas and volumes and compare them to the ratios of the radii, slant heights, and heights.

Concepts

surface area, surface area of prisms, volume, volume of prisms, ratios, proportional reasoning, similar figures, similarity

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Additional Tags

math

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Instructional Ideas

• Have the class investigate if the same ratios that occurred with the prisms also occur with other similar solids

Classroom Considerations

• The class should know how to calculate surface area and volume
• Class members need to be comfortable working with ratios

Pros

• Includes an extension activity based upon Gulliver's Travels
• Contains suggestions for differentiation for those that struggle

Cons

• Both activity sheets reference the incorrect number for one of the problems
• Includes an activity that does not belong with the lesson