Question

The total surface area of a cube is $150{\text{ c}}{{\text{m}}^2}$. Find the perimeter of any one of its faces?

Answer 1

Hint: We have to find the value of the perimeter of any one of the cube faces. In this question, they give the value of the total surface of the cube as a given. We have to find the length of the side in the cube by using the total surface area of a cube. Then we have to calculate the perimeter on any one of its faces. Then we will get the required solution. Here it is given below in the complete step by step solution.

Formula used: A cube has ${\text{6}}$ faces. Its faces are in the shape of a square. The area of the square is the square value of its side (that is ${{\text{l}}^2}$ where if ${\text{l}}$ is the side of the square). Hence,
Total surface area of a cube $ = {\text{ 6 }}{{\text{l}}^2}$ ( in which ${\text{l}}$ is the side of the cube)

Complete step-by-step answer:
Given that the total surface area of a cube is $150{\text{ c}}{{\text{m}}^2}$.

To find that the perimeter of any one of its face
Let Total surface area of cube ${\text{ = 150 c}}{{\text{m}}^2}$
$ \Rightarrow 6{\text{ }}{{\text{l}}^2} = 150$
Here Total surface area of a cube $ = {\text{ 6 }}{{\text{l}}^2}$( in which ${\text{l}}$ is the side of the cube)
$ \Rightarrow {{\text{l}}^2} = \dfrac{{150}}{6}$
Dividing the term, we get
$ \Rightarrow {{\text{l}}^2} = 25$
$ \Rightarrow {\text{l = }}\sqrt {25} $
The value of square root is,
${\text{l = 5}}$
Hence, each side of the cube is $5{\text{ cm}}$.
As we know that each face of the cube is square.
Each edge side of cube ${\text{ = 5 cm}}$
Now, perimeter of one face of cube ${\text{ = 4 }} \times $ side
$ \Rightarrow 4 \times 5$
$ \Rightarrow 20{\text{ cm}}$

$\therefore $ Perimeter of one face of the cube is $20{\text{ cm}}$.

Note: We have to know that in geometry, a cube is a three- dimensional solid object bounded by six square faces with the meeting at each vertex. It has 6 faces, 12 edges, and 8 vertices. The cube is the only regular hexahedron and is one of the five platonic solids. The cube is dual to the octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces are all squares.