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I was searching frustum volume deriving formula on wikipedia. I met this equation on wikipedia. This equation is about deriving frustum from pyramid.

$$\frac{B_1}{h_1^2}=\frac{B_2}{h_2^2}=\frac{\sqrt{B_1 B_2}}{h_1 h_2}=\alpha$$

https://wikimedia.org/api/rest_v1/media/math/render/svg/f6afcd77cd9a486d4cec55eb7fac4a519b0a8b87

Thanks

1 Answers 1

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The bases of a frustum are similar shapes with a (linear) ratio of similarity of $\cfrac{h_1}{h_2}\,$. Their areas will be in proportion of the square of the similarity ratio i.e. $\;\cfrac{B_1}{B_2}=\cfrac{h_1^2}{h_2^2}\,$ which gives the first equality.

The second equality is simply saying that if $a=b \ge 0$ then $\sqrt{a b}=a=b\,$.