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1. Are the two cylinders similar? If so, what is the scale factor of the first figure to the second figure?

   

Take note Theorem 11-12: Areas and Volumes of Similar Solids

If the scale factor of two similar solids is a : b, then

• the ratio of their corresponding areas is a 2 : b 2 eh squared , colon , b squared
• the ratio of their volumes is a 3 : b 3 eh cubed , colon , b cubed

Problem 2 Finding the Scale Factor

The square prisms below are similar. What is the scale factor of the smaller prism to the larger prism?

V = 729  cm 3 v equals 729 . cm cubed

V = 1331  cm 3 v equals , 1331 . cm cubed

a 3 b 3 = 729 1331 The ratio of the volumes is  a 3 : b 3 . a b = 9 11 Take the cube root of each side. table with 2 rows and 4 columns , row1 column 1 , fraction eh cubed , over b cubed end fraction , column 2 equals , column 3 729 over 1331 , column 4 cap the ratio of the volumes is . eh cubed . colon , b cubed , . , row2 column 1 , eh over b , column 2 equals , column 3 9 elevenths , column 4 cap take the cube root of each side. , end table

The scale factor is 9 : 11.

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2. 1. What is the scale factor of two similar prisms with surface areas 144  m 2 144 , m squared  and 324  m 2 ? 324 , m squared , question mark
   2. Reasoning Are any two square prisms similar? Explain.