Make a formula to find the volume V of a rectangular parallelepiped by its full surface S

Make a formula to find the volume V of a rectangular parallelepiped by its full surface S, width in and height h.

Suppose the length of this parallelepiped is a.
The volume of the parallelepiped is: V = a * b * h.
The parallelepiped has six pairwise equal faces, the areas of which are equal: ab, ah, hb. Therefore, its surface area is: S = 2ab + 2ah + 2bh. Let us express from this expression a:
S = a (2b + 2h) + 2bh,
S-2bh = a (2b + 2h),
a = (S-2bh) / 2 (b + h).
Substitute the obtained value a into the formula for the volume of the parallelepiped:
V = a * b * h,
V = (S-2bh) * b * h / 2 (b + h).

Answer: V = (S-2bh) * b * h / 2 (b + h).



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