Calculate the sum of the lengths of all the edges of the cube, the edge of which is 4m 6cm.

The problem is given a cube ABCDA1B1C1D1. By definition, all edges of a cube are equal. Let us denote the length of the edge by a. By the condition of the problem:

a = 4 m 6 cm;

In the problem, you need to find the sum of the lengths L of all edges of the cube.

Counting the number of ribs
The cube has six faces. In our case, these are:

Bottom base ABCD;
Upper base A1B1C1D1;
Four side faces AA1B1B; BB1C1C; CC1D1D; DD1A1A.
Each face of a cube is a square, which, respectively, has four equal sides. Multiplying the number of sides in each face by the number of faces themselves, we get:

4 * 6 = 24;

This number is exactly twice the number of edges in the cube, since each edge belongs to two faces at the same time and, accordingly, was counted twice. So the cube has:

24/2 = 12;

ribs and this:

AB; BC; CD; AD; A1B1; B1C1; C1D1; A1D1; AA1; BB1; CC1; DD1;

Calculating the sum of the lengths L of all edges of a cube
Considering that all 12 edges are equal, then:

L = 12 * a;

To calculate this sum, we express the length of the edge a using one unit of measurement. It can be, for example, both meters and centimeters. Knowing that:

1 m = 100 cm;

1 cm = 0.01 m;

we get:

a = 4 m 6 cm = 4 * 100 + 6 = 406 (cm);

or

a = 4 m 6 cm = 4 + 6 * 0.01 = 4.06 (m);

Find L:

L = 12 * a = 12 * 406 = 4872 (cm) = 48 m 72 cm;

or

L = 12 * a = 12 * 4.06 = 48.72 (m) = 48 m 72 cm;

Answer: the sum of the lengths of all the ribs is 48 m 72 cm.