A Surface Area of Similar Solids

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Presentation transcript:

A Surface Area of Similar Solids What is a similar solid? How do you find the ratio of the surface area of two similar solids without calculating the surface area of the two solids?

Similar Figures Similar two dimensional figures have the same shape and 1. The lengths of the corresponding sides are proportional. 2. The corresponding angles are congruent 10 8 5 4 3 6

Similar Solids Similar solids have the same shape and 15 24 10 16 Similar Solids Similar solids have the same shape and 1. The lengths of the corresponding sides are proportional. 2. The corresponding angles are congruent The similarity ratio is 2/3

Surface Area of Similar Solids 15 24 10 16 SA = 2 π r H+2 π r2 Small cylinder SA = 2π(10)(16)+2π(10)2 SA = 320π + 200π SA = 520π Large cylinder SA = 2π(15)(24)+2π(15)2 SA = 720π+450π SA = 1170π

OR… 15 24 10 16 Since the similarity ratio is 2/3, then….

Cross Sectional Area In general, the strength of a given material is proportional to its cross-sectional area. See page 649. Suppose one animal is 4 times as large as another. (Their similarity ratio is 4/1.) How many times stronger are the larger animal’s legs? The larger animal’s legs are 16 times stronger.

Find the similarity ratio of the pyramid on the left to the pyramid on the right. 5 2 Find the ratio of their surface areas.

A support beam for a ceiling is 6 in. wide and 6 in. high A support beam for a ceiling is 6 in. wide and 6 in. high. If you need a second beam with a similar cross section that is 9 times as strong, what should its dimensions be? (?)2 = 9 ? = 3 (3)(6) = 18 18 in × 18 in.

Theorem Similarity ratio ( )1 SA ratio ( )2 The ratio of the surface areas of two similar solids is the square of their similarity ratio. Similarity ratio ( )1 SA ratio ( )2

What is a similar solid? Similar solids have the same shape and 1. The lengths of the corresponding sides are proportional. 2. The corresponding angles are congruent How do you find the ratio of the surface area of two similar solids without calculating the surface area of the two solids? Square the similarity ratio. ( )2

Assignment 9-3A Page 650, 1-7, 16-23 #16-19 no formulas with numbers no credit