Given:
The volume of a cube-shaped box is [tex]\dfrac{1}{8}[/tex] cubic meter.
To find:
The perimeter of each of its faces.
Solution:
Let "a" be the side length of the cube shaped box. Then the volume of the box is:
[tex]V=(side)^3[/tex]
[tex]V=a^3[/tex]
It is given that the volume of a cube-shaped box is [tex]\dfrac{1}{8}[/tex] cubic meter.
[tex]a^3=\dfrac{1}{8}[/tex]
Taking cube root on both sides, we get
[tex]a=\dfrac{1}{2}[/tex]
Now, the perimeter of each face of a cube is:
[tex]P=4a[/tex]
Where, a is the side length of the cube.
Putting [tex]a=\dfrac{1}{2}[/tex], we get
[tex]P=4\times \dfrac{1}{2}[/tex]
[tex]P=2[/tex]
Therefore, the perimeter of each face of a cube-shaped box is 2 meters.
