Measurements of a rectangular parallelepiped are 4cm, 6cm, 9cm. Find an edge of a cube whose
| September 8, 2021 | education
Measurements of a rectangular parallelepiped are 4cm, 6cm, 9cm. Find an edge of a cube whose volume is equal to the volume of this parallelepiped.
Knowing the lengths of all three dimensions of the parallelepiped, we determine its volume.
V = a * b * c = 4 * 6 * 9 = 216 cm3.
Since the lengths of all edges of a cube are equal, its volume will be equal to: Vcube = a ^ 3.
By condition, the volume of the cube is equal to the volume of the parallelepiped, then a ^ 3 = 215.
A = 3√216 = 6 cm.
Answer: The length of the edge of the cube is 6 cm.
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