The total surface area of a rectangular parallelepiped, at the base of which a rectangle with sides of 9 cm and 6 cm, is 408 cm2. Find the volume of a parallelepiped.
The total surface area of a rectangular parallelepiped consists of the sum of the areas of all its faces, two of which can be considered bases, the other four – lateral. The lateral surface area is equal to the product of the height and the perimeter of the base.
S = 2 * Sb + S side = 2 * Sb + h * P, from here we find the height of the parallelepiped:
h = (S-2 * Ssn) / P = (408-2 * 9 * 6) / (9 + 9 + 6 + 6) = (408-108) / 30 = 300/30 = 10 cm.
The volume of a parallelepiped is equal to the product of its three dimensions:
V = 9 * 6 * 10 = 540 cm3.
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