The sum of the lengths of all the edges of the rectangular parallelepiped is equal to 84 cm of its lengths 9 cm width 7 cm find the volume of the parallelepiped.
P (ABCDA1B1C1D1) = 84 cm
AD = BC = A1D1 = B1C1 = 9 cm
AB = DC = A1B1 = D1C1 = 7 cm
V (ABCDA1B1C1D1) -?
1) The perimeter of a rectangular parallelepiped is calculated using the following formula:
P (ABCDA1B1C1D1) = 4 * AD + 4 * AB + 4 * AA1;
2) Calculate the height of the rectangular parallelepiped:
AA1 = (P (ABCDA1B1C1D1) – 4 * AD – 4 * AB) / 4 = (84 – 4 * 9 – 4 * 7) / 4 = 5 (cm);
3) Calculate the volume of a rectangular parallelepiped:
V (ABCDA1B1C1D1) = AD * AB * AA1 = 9 * 7 * 5 = 315 (cm3).
Answer: The volume of a rectangular parallelepiped is 315 cm3.
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