The dimensions of a rectangular parallelepiped are expressed in prime numbers. its volume is

| September 29, 2021 | education

The dimensions of a rectangular parallelepiped are expressed in prime numbers. its volume is 1) 66 cm3. 2) 195 cm3. 3) 255 cm3. What are the dimensions of a rectangular parallelepiped?

Let’s denote the measurements of this rectangular parallelepiped through x1, x2 and x3.
The volume V of a rectangular parallelepiped can be determined in the formula:
V = x1 * x2 * x3.
According to the condition of the problem, the measurements of a given rectangular parallelepiped are expressed in prime numbers.
Therefore, in order to find the dimensions of a given rectangular parallelepiped, you need to decompose the number V into the product of three prime factors.
1)
V = 66 cm³.
66 = 11 * 6 = 11 * 3 * 2.
Therefore, the measurements of this rectangular parallelepiped are 11 cm, 3 cm and 2 cm.
2)
V = 195 cm³.
195 = 5 * 49 = 5 * 7 * 7.
Therefore, the measurements of this rectangular parallelepiped are 5 cm, 7 cm and 7 cm.
3)
V = 255 cm³.
255 = 5 * 51 = 5 * 3 * 17.
Therefore, the measurements of this rectangular parallelepiped are 5 cm, 3 cm and 17 cm.



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