Question 1112480
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In any two similar figures, if the ratio of linear measurements (scale factor) is a:b, then the ratio of area measurements is a^2:b^2, and the ratio of volume measurements is a^3:b^3.<br>
In this problem you know the ratio of areas is 1:5; that means the scale factor is 1:sqrt(5), and the ratio of volumes is 1:5*sqrt(5).  So given that the volume of the larger pyramid is 100 cm^3, the volume of the smaller is
{{{100/(5*sqrt(5)) = 4*sqrt(5)}}}