Three edges of a rectangular parallelepiped that go out from one vertex are equal to 1, 4 and 2
| April 8, 2021 | education
Three edges of a rectangular parallelepiped that go out from one vertex are equal to 1, 4 and 2. Find an edge of a cube of the same size.
Determine the volume of the parallelepiped ABCDA1B1C1D1.
V = AA1 * AB * AD = 2 * 1 * 4 = 8 cm3.
Since the cube is of equal size, its volume is equal to the volume of the parallelepiped.
In a cube, all edges are equal, then its volume is:
V = AB ^ 3.
AB = 3√8 = 2 cm.
Answer: The edge of an equal-sized cube is 2 cm.
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