Math

The surface areas of two similar solids are 416yd ^2 and 1,354yd ^2. The volume of the larger solid is 2,976 yd^3. What is the volume of the smaller solid?
2,976 yd ^3
2,619 yd ^3
914 yd ^3
507 yd ^2

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  1. The areas of similar objects are proportional to the square of their sides
    so 416/1354 = x^2/y^2 , where x and y are corresponding sides , x as the smaller
    x^2/y^2 = 416/1354 = 208/677
    x/y = √208/√677

    the volumes of similar objects are proportional to the cubes of their corresponding sides
    x^3/y^3 = volume/2976
    (√208)^3 / (√677)^3 = volume/2976
    volume = appr 506.8 yds^3

    Your answer has yds^2, clearly a typo

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