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The areas of the bases of two similar cones are in the ratio of 9:16 Find the ratio of...

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aa42 | Student, Grade 10 | (Level 1) Honors

Posted October 23, 2012 at 5:02 PM via web

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The areas of the bases of two similar cones are in the ratio of 9:16

Find the ratio of the heights of the cones

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted October 23, 2012 at 9:50 PM (Answer #1)

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Since the ratios of the areas of the bases is 9:16 the scale factor is 3:4. Thus the ratio of the heights is 3:4.

** If the ratio of corresponding areas of two similar figures is `a^2:b^2` , then the ratio of corresponding lengths (the scale factor) is `a:b` **

The ratio of their volumes will be `a^3:b^3`

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