Question

Куб має об'єм удвічі більший за об'єм прямокутного паралелепіпеда. Знайдіть суму довжин усіх ребер куба, якщо виміри прямокутного паралелепіпеда дорівнюють 2 см, 2 см, 1 см.

Answer 1

Знаходимо об'єм прямокутного паралелепіпеда
V=2*2*1=4 cм^3

Тоді об'єм куба має бути 8 cм^3
a*a*a=8 <-> a^3=8 <-> a=2 cм

В кубі 12 ребер, кожне по 2 см
12*2=24 см

Відповідь: сума довжин всіх ребер куба 24см

Answer 2

Calculation of the Volume of a Cube and a Rectangular Parallelepiped

To find the sum of the lengths of all the edges of a cube, we first need to determine the volume of the cube and the rectangular parallelepiped.

Let's assume the dimensions of the rectangular parallelepiped are 2 cm, 2 cm, and 1 cm.

The volume of a rectangular parallelepiped is given by the formula:

Volume = length × width × height

Substituting the given dimensions, we have:

Volume of the rectangular parallelepiped = 2 cm × 2 cm × 1 cm = 4 cm³.

Now, according to the given statement, the volume of the cube is twice that of the rectangular parallelepiped. Therefore, the volume of the cube is:

Volume of the cube = 2 × Volume of the rectangular parallelepiped = 2 × 4 cm³ = 8 cm³.

Calculation of the Sum of the Lengths of all Edges of the Cube

To find the sum of the lengths of all the edges of the cube, we need to determine the length of one edge first.

The formula to calculate the length of one edge of a cube is:

Length of one edge = ∛(Volume of the cube)

Substituting the volume of the cube, we have:

Length of one edge = ∛(8 cm³) = 2 cm.

Since a cube has 12 edges of equal length, the sum of the lengths of all the edges of the cube is:

Sum of lengths of all edges of the cube = 12 × Length of one edge = 12 × 2 cm = 24 cm.

Therefore, the sum of the lengths of all the edges of the cube is 24 cm.

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