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18 July, 05:09

20. The surface areas of two similar solids are 216 m² and 1014 m². The volume of the larger one is 2197 m³. What is the volume of the smaller one?

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  1. 18 July, 05:25
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    216 m³

    Step-by-step explanation:

    The ratio of linear dimensions is the square root of the ratio of area dimensions.

    s = √ (216/1014) = √ (36/169) = 6/13

    Then the ratio of volume dimensions is the cube of that. The smaller volume is ...

    v = (6/13) ³·2197 m³ = 216/2197·2197 m³ = 216 m³

    The volume of the smaller solid is 216 m³.
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