The length of the first rectangular parallelepiped is 8 times the length of the second, the width of the first

| September 5, 2021 | education

The length of the first rectangular parallelepiped is 8 times the length of the second, the width of the first is 6 times less than the width of the second, and the height of the first is 4 times greater than the height of the second. The volume of which of the parallelepipeds is larger and how many times?

Let the length of the first parallelepiped be X cm, then the length of the second parallelepiped will be equal to X / 8 cm.

The width of the first parallelepiped is denoted by Y cm, then the width of the second will be equal to 6 * Y cm.

The height of the first parallelepiped is denoted by Z cm, then the height of the second will be equal to X / 4 cm.

The volume of the first parallelepiped is V1 = X * Y * Z cm3.

The volume of the second parallelepiped is V2 = (X / 8) * 6 * Y * (X / 4) = (3/16) * X * Y * Z cm3.

V1 / V2 = X * Y * Z / = (3/16) * X * Y * Z.

V1 = V2 * 16/3 = 5 (1/3).

Answer: The volume of the first parallelepiped is 5 (1/3) times larger.



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