Question

Знайдіть ребро куба якщо його об'єм дорівнює об'єму прямокутного паралелепіпеда з вимірами 6 12 і 3

Answer 1

Ответ:

длина ребра куба а=6

Пошаговое объяснение:

V куба = V прямоугольного параллелепипеда

V прямоугольного параллелепипеда=a×b×c

a=6

b=12

c=3

V прямоугольного параллелепипеда=6×12×3=216

=> V куба=216

V куба =a^3

a^3=216

a^3=6^3

a=6

Answer 2

Finding the Edge Length of a Cube with Equal Volume to a Rectangular Parallelepiped

To find the edge length of a cube when its volume is equal to the volume of a rectangular parallelepiped, we can use the formula for volume. The formula for the volume of a cube is given by:

Volume of a Cube = (Edge Length)^3

Similarly, the formula for the volume of a rectangular parallelepiped is given by:

Volume of a Rectangular Parallelepiped = Length x Width x Height

In this case, we are given the dimensions of the rectangular parallelepiped as 6, 12, and 3. Let's denote the edge length of the cube as 'x'. We can set up the equation:

(Edge Length of Cube)^3 = (Length of Rectangular Parallelepiped) x (Width of Rectangular Parallelepiped) x (Height of Rectangular Parallelepiped)

Substituting the given values, we have:

x^3 = 6 x 12 x 3

Simplifying the equation:

x^3 = 216

To find the value of 'x', we need to take the cube root of both sides of the equation:

x = ∛216

Calculating the cube root of 216, we find:

x ≈ 6

Therefore, the edge length of the cube is approximately 6 units.

Please note that the above calculation is based on the given information and assumes that the rectangular parallelepiped and the cube have the same volume.