Find the volume of the cube if the perimeter of one face is 20 dm.

1) Find the edge of the cube.
The face of the cube is a square, which means that the edge of the cube is the side of the square. We need to find the side of the square, knowing its perimeter.
A square is a quadrangle in which all sides are equal and the corners are straight.
The perimeter of any geometric shape is the sum of the lengths of all its sides. Let’s write the formula for the perimeter of the square:
P = 4 × a,
where P is the perimeter, and is the length of the side of the square.
From the formula for the perimeter of a square, we express its side:
a = P: 4.
We calculate the length of the side of the square, substituting the value of the perimeter into the formula:
a = 20: 4 = 5 dm.
2) Find the volume of the cube.
A cube (hexahedron) is a regular polyhedron, each face of which is a square.
To calculate the volume of a cube, you need to raise its side to the third power. Let’s write the formula:
V = a³,
where a is the edge of the cube, V is the volume of the cube.
Substituting the value of the edge of the cube into the formula, we find the volume of the cube:
V = 5³ = 125 cm³.
Answer: the volume of the cube is 125 cm³.