# The volume of a rectangular parallelopiped is equal to prime numbers.

September 12, 2021 | education

| **The volume of a rectangular parallelopiped is equal to prime numbers. volume is 385 cm3. find the volume of the surface of a rectangular parallelopiped**

Let’s expand 385 into prime factors:

385 = 5 * 77 = 5 * 7 * 11.

Since the lengths of the faces of a rectangular parallelepiped with a volume of 385 cm³ are prime numbers, the lengths of these faces are 5 cm, 7 cm and 11 cm.

Let’s calculate the surface area of a given rectangular parallelepiped:

2 * (5 * 7 + 7 * 11 + 5 * 11) = 2 * (35 + 77 + 55) = 2 * 167 = 334 (cm²).

Answer: 334 cm².

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