A rectangular parallelepiped is equal to the volume of a cube with an edge of 4 dm.

| September 3, 2021 | education

A rectangular parallelepiped is equal to the volume of a cube with an edge of 4 dm. The length of the parallelepiped is 5 whole 1/3 dm, and the width is 2 times less than the length. How many decimeters is the height of the parallelepiped greater than its width?

1) Calculate the volume of a cube with an edge of 4 dm:

4 * 4 * 4 = 64 dm ^ 3.

2) The volume of a rectangular parallelepiped is equal to the volume of this cube, that is, it is 64 dm ^ 3.

3) Determine the width of the base of the parallelepiped:

5 1/3: 2 = 16/3 * 1/2 = 8/3 = 2 2/3 dm.

4) Find the area of ​​the base of the parallelepiped by multiplying its length by width:

5 1/3 * 2 2/3 = 16/3 * 8/3 = 128/9 = 14 2/9 dm ^ 2.

5) Calculate the height of a given parallelepiped, dividing its volume by the area of ​​the base:

64: 14 2/9 = 64: 128/9 = 64 * 9/128 = 9/2 = 4 1/2 dm.

6) How many decimeters is the height of the parallelepiped greater than its width:

4 1/2 – 2 2/3 = (4 – 2) + (1/2 – 2/3) = 2 + (3/6 – 4/6) = 2 – 1/6 = 1 5/6 dm.

Answer: 1 5/6 dm.



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