Question

The perimeter of one face of the cube is 40 cm. Find the sum of length of the edges.

Answer 1

Hint: The knowledge of a cube, its faces , vertices and edges will be used. A cube has 6 faces, 12 edges and 8 vertices. Also, the perimeter of a face is equal to the sum of four edges. We can start by assuming that the length of one edge is x cm and then form an equation using the given data that the perimeter of one of the faces of the cube is 40 cm. After getting the value of x, we can then find the sum of length of all edges.

Complete step-by-step answer:

Let the length of one edge be x cm, then the perimeter of one face is given by the sum of its four sides. The cube has a face with the shape of the square, so all its edges are equal. So we can write that-
$x + x + x + x = 40 cm$
$4x = 40$
$x = 10 cm$

This is the length of a single edge. There are 12 edges in a cube so the total length will be 12 times the length of one edge. In the figure we can see that four edges are on the front, 2 on top, 2 on bottom, and 4 more behind the cube.
Total length = $10 \times 12$
Total length of the edges is 120 cm
This is the required answer.

Note:In such types of questions mainly the definition and properties of 2-D and 3-D figures. One common mistake is that students forget to write the units in the final answer, which should be avoided. We just need to understand the language of the question, check what is asked, and then form the equation. After finding the value of x, students must be careful that the sum of length of all edges is asked and not if a single face.